[1] Abakumov, E.V. 1995. Cyclicity and approximation by lacunary power series. Michigan Math. J., 42(2), 277–299.Google Scholar

[2] Agler, J. and McCarthy, J. E. 2002. Pick Interpolation and Hilbert Function Spaces. Graduate Studies in Mathematics, vol. 44. Providence, RI: American Mathematical Society.

[3] Ahern, P. R. and Clark, D. N. 1970a. On functions orthogonal to invariant subspaces. Acta Math., 124, 191–204.Google Scholar

[4] Ahern, P. R. and Clark, D. N. 1970b. Radial limits and invariant subspaces. Amer. J. Math., 92, 332–342.Google Scholar

[5] Ahern, P.R. and Clark, D. N. 1971. Radial nth derivatives of Blaschke products. Math. Scand., 28, 189–201.Google Scholar

[6] Akhiezer, N. I. and Glazman, I. M. 1993. Theory of Linear Operators in Hilbert Space. New York: Dover Publications. Translated from the Russian and with a preface by Merlynd Nestell, reprint of the 1961 and 1963 translations, two volumes bound as one.

[7] Aleksandrov, A. B. 1987. Multiplicity of boundary values of inner functions. Izv. Akad. Nauk Armyan. SSR Ser. Mat., 22(5), 490–503, 515.Google Scholar

[8] Aleksandrov, A. B. 1989. Inner functions and related spaces of pseudocontinuable functions. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 170(17), 7–33, 321.Google Scholar

[9] Aleksandrov, A. B. 1995. On the existence of angular boundary values of pseudocontinuable functions. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 222(23), 5–17, 307.Google Scholar

[10] Aleksandrov, A. B. 1996. Isometric embeddings of co-invariant subspaces of the shift operator. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 232(24), 5–15, 213.Google Scholar

[11] Aleksandrov, A. B. 1997. Gap series and pseudocontinuations: an arithmetic approach. Algebra i Analiz, 9(1), 3–31.Google Scholar

[12] Aleksandrov, A. B. 1999. Embedding theorems for coinvariant subspaces of the shift operator. II. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 262(27), 5–48, 231.Google Scholar

[13] Aleman, A. and Richter, S. 1996. Simply invariant subspaces of H2 of some multiply connected regions. Integral Equations Operator Theory, 24(2), 127–155.Google Scholar

[14] Aleman, A. and Ross, W. T. 1996. The backward shift on weighted Bergman spaces. Michigan Math. J., 43(2), 291–319.Google Scholar

[15] Aleman, A., Richter, S. and Ross, W. T. 1998. Pseudocontinuations and the backward shift. Indiana Univ. Math. J., 47(1), 223–276.Google Scholar

[16] Aleman, A., Feldman, N. S., and Ross, W. T. 2009. The Hardy Space of a Slit Domain. Frontiers in Mathematics. Basel: Birkhäuser Verlag.

[17] Arias de Reyna, J. 2002. Pointwise Convergence of Fourier Series. Lecture Notes in Mathematics, vol. 1785. Berlin: Springer-Verlag.

[18] Aronszajn, N. 1950. Theory of reproducing kernels. Trans. Amer. Math. Soc., 68, 337–404.Google Scholar

[19] Arov, D. Z. 1971. Darlington's method in the study of dissipative systems. Dokl. Akad. Nauk SSSR, 201(3), 559–562.Google Scholar

[20] Arveson, W. 2002. A Short Course on Spectral Theory. Graduate Texts in Mathematics, vol. 209. New York: Springer-Verlag.

[21] Bagemihl, F. and Seidel, W. 1954. Some boundary properties of analytic functions. Math. Z., 61, 186–199.Google Scholar

[22] Ball, J. 1973. Unitary perturbations of contractions. Ph.D. thesis, University of Virginia.

[23] Ball, J. A. and Lubin, A. 1976. On a class of contractive perturbations of restricted shifts. Pacific J. Math., 63(2), 309–323.Google Scholar

[24] Baranov, A. I., Chalendar, E., Fricain, E., Mashreghi, J., and Timotin, D. 2010. Bounded symbols and reproducing kernel thesis for truncated Toeplitz operators. J. Funct. Anal., 259(10), 2673–2701.Google Scholar

[25] Baranov, A., Bessonov, R. and Kapustin, V. 2011. Symbols of truncated Toeplitz operators. J. Funct. Anal., 261(12), 3437–3456.Google Scholar

[26] Bari, N. K. 1951. Biorthogonal systems and bases in Hilbert space. Moskov. Gos. Univ. U?cenye Zapiski Matematika, 148(4), 69–107.Google Scholar

[27] Bercovici, H. 1988. Operator Theory and Arithmetic in H8. Mathematical Surveys and Monographs, vol. 26. Providence, RI: American Mathematical Society.

[28] Berman, R. D. and Cohn, W. S. 1987. Tangential limits of Blaschke products and functions of bounded mean oscillation. Illinois J. Math., 31(2), 218–239.Google Scholar

[29] Bessonov, R. V. 2014. Truncated Toeplitz operators of finite rank. Proc. Amer. Math. Soc., 142(4), 1301–1313.Google Scholar

[30] Beurling, A. 1948. On two problems concerning linear transformations in Hilbert space. Acta Math., 81, 17.Google Scholar

[31] Blandignéres, A., Fricain, E., Gaunard, F., Hartmann, A. and Ross, W. 2013. Reverse Carleson embeddings for model spaces. J. Lond. Math. Soc. (2), 88(2), 437–464.Google Scholar

[32] Boas, Jr., R. P. 1941. A general moment problem. Amer. J. Math., 63, 361–370.Google Scholar

[33] Böttcher, A. and Silbermann, B. 2006. Analysis of Toeplitz Operators, 2nd edn. SpringerMonographs in Mathematics. Berlin: Springer-Verlag. Prepared jointly with Alexei Karlovich.

[34] Brown, A. and Halmos, P. R. 1963/1964. Algebraic properties of Toeplitz operators. J. Reine Angew. Math., 213, 89–102.Google Scholar

[35] Brown, L., and Shields,, A. L. 1984. Cyclic vectors in the Dirichlet space. Trans. Amer. Math. Soc., 285(1), 269–303.Google Scholar

[36] Cargo, G. T. 1962. Angular and tangential limits of Blaschke products and their successive derivatives. Canad. J. Math., 14, 334–348.Google Scholar

[37] Chalendar, I. and Timotin, D. Commutation relations for truncated Toeplitz operators. arXiv:1305.6739.

[38] Chalendar, I., Fricain, E., and Timotin, D. 2009. On an extremal problem of Garcia and Ross. Oper. Matrices, 3(4), 541–546.Google Scholar

[39] Chevrot, N., Fricain, E., and Timotin, D. 2007. The characteristic function of a complex symmetric contraction. Proc. Amer. Math. Soc., 135(9), 2877–2886 (electronic).Google Scholar

[40] Christensen, O. 2003. An Introduction to Frames and Riesz Bases. Applied and Numerical Harmonic Analysis. Boston, MA: Birkhäuser Boston Inc.

[41] Cima, J.A. and Ross, W. T. 2000. The Backward Shift on the Hardy Space. Mathematical Surveys and Monographs, vol. 79. Providence, RI: American Mathematical Society.

[42] Cima, J.A., Matheson, A. L., and Ross, W. T. 2006. The Cauchy Transform. Mathematical Surveys and Monographs, vol. 125. Providence, RI: American Mathematical Society.

[43] Cima, J.A., Ross, W. T., and Wogen, W. R. 2008. Truncated Toeplitz operators on finite dimensional spaces. Oper. Matrices, 2(3), 357–369.Google Scholar

[44] Cima, J.A. and Matheson, A. L. 1997. Essential norms of composition operators and Aleksandrov measures. Pacific J. Math., 179(1), 59–64.Google Scholar

[45] Cima, J.A., Garcia, S. R., Ross, W. T., and Wogen, W. R. 2010. Truncated Toeplitz operators: spatial isomorphism, unitary equivalence, and similarity. Indiana Univ. Math. J., 59(2), 595–620.Google Scholar

[46] Clark, D. N. 1972. One dimensional perturbations of restricted shifts. J. Analyse Math., 25, 169–191.Google Scholar

[47] Coburn|L. A. 1967. The C*-algebra generated by an isometry. Bull. Amer. Math. Soc., 73, 722–726.

[48] Coburn, L.A. 1969. The C*-algebra generated by an isometry. II. Trans. Amer. Math. Soc., 137, 211–217.Google Scholar

[49] Cohn, B. 1982. Carleson measures for functions orthogonal to invariant subspaces. Pacific J. Math., 103(2), 347–364.Google Scholar

[50] Collingwood, E. F. and Lohwater, A. J. 1966. The Theory of Cluster Sets. Cambridge Tracts in Mathematics and Mathematical Physics, No. 56. Cambridge: Cambridge University Press.

[51] Conway, J. B. 1990. A Course in Functional Analysis, 2nd edn. Graduate Texts in Mathematics, vol. 96. New York: Springer-Verlag.

[52] Conway, J. B. 2000. A Course in Operator Theory. Graduate Studies in Mathematics, vol. 21. Providence, RI: American Mathematical Society.

[53] Cowen, C. and MacCluer, B. D. 1995. Composition Operators on Spaces of Analytic Functions. Studies in Advanced Mathematics. Boca Raton, FL: CRC Press.

[54] Crofoot, R.B. 1994. Multipliers between invariant subspaces of the backward shift. Pacific J. Math., 166(2), 225–246.Google Scholar

[55] Danciger, J., Garcia, S. R., and Putinar, M. 2008. Variational principles for symmetric bilinear forms. Math. Nachr., 281(6), 786–802.Google Scholar

[56] Davidson, K. R. 1996. C*-algebras by example. Fields Institute Monographs, vol. 6. Providence, RI: American Mathematical Society.

[57] de Branges, L. 1968. Hilbert Spaces of Entire Functions. Englewood Cliffs, NJ: Prentice-Hall.

[58] de Branges, L. and Rovnyak, J. 1966. Square Summable Power Series. London: Holt, Rinehart and Winston.

[59] Douglas, R.G. 1998. Banach Algebra Techniques in Operator Theory, 2nd edn. Graduate Texts in Mathematics, vol. 179. New York: Springer-Verlag.

[60] Douglas, R.G., and Helton, J.W. 1973. Inner dilations of analytic matrix functions and Darlington synthesis. Acta Sci. Math. (Szeged), 34, 61–67.Google Scholar

[61] Douglas, R. G., Shapiro, H. S., and Shields, A. L. 1970. Cyclic vectors and invariant subspaces for the backward shift operator. Ann. Inst. Fourier (Grenoble), 20(1), 37–76.Google Scholar

[62] Douglas, R. G. 1972. Banach Algebra Techniques in Operator Theory. Pure and Applied Mathematics, vol. 49. New York: Academic Press.

[63] Duren, P. L. 1970. Theory of Hp Spaces. New York: Academic Press.

[64] Duren, P. and Schuster, A. 2004. Bergman Spaces. Mathematical Surveys and Monographs, vol. 100. Providence, RI: American Mathematical Society.

[65] Dyakonov, K. and Khavinson, D. 2006. Smooth functions in star-invariant subspaces. In Recent Advances in Operator-Related Function Theory. Contemporary Mathematics, vol. 393. Providence, RI: American Mathematical Society, pp. 59–66.

[66] Dyakonov, K. M. 2000. Kernels of Toeplitz operators via Bourgain's factorization theorem. J. Funct. Anal., 170(1), 93–106.Google Scholar

[67] Dyakonov, K. M. 2012. Zeros of analytic functions, with or without multiplicities. Math. Ann., 352(3), 625–641.Google Scholar

[68] Dyakonov, K. M. 2014. Two problems on coinvariant subspaces of the shift operator. Integral Equations Operator Theory, 78(2), 151–154.Google Scholar

[69] Ebbinghaus, H.-D., Hermes, H., Hirzebruch, F., Koecher, M., Mainzer, K., Neukirch, J., Prestel, A., and Remmert, R. 1991. Numbers. Graduate Texts in Mathematics, vol. 123. New York: Springer-Verlag. Translated from the second 1988 German edition by H. L. S., Orde.

[70] El-Fallah, O., Kellay, K., Mashreghi, J., and Ransford, T. 2014. A Primer on the Dirichlet Space. Cambridge Tracts in Mathematics, vol. 203. Cambridge: Cambridge University Press.

[71] Erdélyi, I. 1966. On partial isometries in finite-dimensional Euclidean spaces. SIAM J. Appl. Math., 14, 453–467.Google Scholar

[72] Fabry, E.1898–1899. Sur les séries de Taylor qui ont une infinité de points singuliers. Acta Math., 22, 65–88.

[73] Fricain, E., and Mashreghi, J. 2014. The Theory of H(b) spaces, Volume 1. New Mathematical Monographs, vol. 20. Cambridge: Cambridge University Press.

[74] Fricain, E., and Mashreghi, J. 2015. The Theory of H(b) Spaces, Volume 2. New Mathematical Monographs, vol. 21. Cambridge: Cambridge University Press.

[75] Frostman, O. 1942. Sur les produits de Blaschke. Kungl. Fysiografiska Sällskapets i Lund Förhandlingar [Proc. Roy. Physiog. Soc. Lund], 12(15), 169–182.Google Scholar

[76] Fuhrmann, P. A. 1968. On the corona theorem and its application to spectral problems in Hilbert space. Trans. Amer. Math. Soc., 132, 55–66.Google Scholar

[77] Fuhrmann, P. A. 1976. Exact controllability and observability and realization theory in Hilbert space. J. Math. Anal. Appl., 53(2), 377–392.Google Scholar

[78] Garcia, S. R. 2006. Conjugation and Clark operators. In Recent Advances in Operator-related Function Theory. Contemporary Mathematics, vol. 393. Providence, RI: American Mathematical Society, pp. 67–111.

[79] Garcia, S. R. 2008a. Aluthge transforms of complex symmetric operators. Integral Equations Operator Theory, 60(3), 357–367.Google Scholar

[80] Garcia, S. R. and Putinar, M. 2006. Complex symmetric operators and applications. Trans. Amer. Math. Soc., 358(3), 1285–1315 (electronic).Google Scholar

[81] Garcia, S. R. and Putinar, M. 2007. Complex symmetric operators and applications. II. Trans. Amer. Math. Soc., 359(8), 3913–3931 (electronic).Google Scholar

[82] Garcia, S. R. and Wogen, W. R. 2009. Complex symmetric partial isometries. J. Funct. Anal., 257(4), 1251–1260.Google Scholar

[83] Garcia, S. R. and Wogen, W. R. 2010. Some new classes of complex symmetric operators. Trans. Amer. Math. Soc., 362(11), 6065–6077.Google Scholar

[84] Garcia, S. R. and Putinar, M. 2008. Interpolation and complex symmetry. Tohoku Math. J. (2), 60(3), 423–440.Google Scholar

[85] Garcia, S. R. 2005a. A *-closed subalgebra of the Smirnov class. Proc. Amer. Math. Soc., 133(7), 2051–2059 (electronic).Google Scholar

[86] Garcia, S. R. 2005b. Conjugation, the backward shift, and Toeplitz kernels. J. Operator Theory, 54(2), 239–250.Google Scholar

[87] Garcia, S. R. 2005c. Inner matrices and Darlington synthesis. Methods Funct. Anal. Topology, 11(1), 37–47.Google Scholar

[88] Garcia, S. R. 2008b. The eigenstructure of complex symmetric operators. Pages 169–183 of: Recent advances in matrix and operator theory. Oper. TheoryAdv. Appl., vol. 179. Basel: Birkhäuser.

[89] Garcia, S. R. and Poore, D. E. 2013a. On the closure of the complex symmetric operators: compact operators and weighted shifts. J. Funct. Anal., 264(3), 691–712.Google Scholar

[90] Garcia, S. R. and Poore, D. E. 2013b. On the norm closure problem for complex symmetric operators. Proc. Amer. Math. Soc., 141(2), 549.Google Scholar

[91] Garcia, S. R. and Ross, W. T. 2009. A non-linear extremal problem on the Hardy space. Comput. Methods Funct. Theory, 9(2), 485–524.Google Scholar

[92] Garcia, S. R. and Ross, W. T. 2010. The norm of a truncated Toeplitz operator. In Hilbert Spaces of Analytic Functions. CRM Proc. Lecture Notes, vol. 51. Providence, RI: American Mathematical Society, pp. 59–64.

[93] Garcia, S. R. and Ross, W. T. 2013. Recent progress on truncated Toeplitz operators. In Blaschke Products and their Applications. Fields Institute Communications, vol. 65. New York: Springer, pp. 275–319.

[94] Garcia, S. R. and Sarason, D. 2003. Real outer functions. Indiana Univ. Math. J., 52(6), 1397–1412.Google Scholar

[95] Garcia, S.R., Ross, W. T., and Wogen, W. R. 2010a. Spatial isomorphisms of algebras of truncated Toeplitz operators. Indiana Univ. Math. J., 59(6), 1971– 2000.Google Scholar

[96] Garcia, S. R., Ross, W. T., and Wogen, W. R. 2010b. Spatial isomorphisms of algebras of truncated Toeplitz operators. Indiana Univ. Math. J., 59(6), 1971– 2000.Google Scholar

[97] Garnett, J. 2007. Bounded Analytic Functions. Graduate Texts in Mathematics, vol. 236. New York: Springer.

[98] Gilbreath, T. M. and Wogen, W. R. 2007. Remarks on the structure of complex symmetric operators. Integral Equations Operator Theory, 59(4), 585–590.Google Scholar

[99] Gohberg, I.C. and Krupnik, N. Ja. 1969. The algebra generated by the Toeplitz matrices. Funkcional. Anal. i Priložen., 3(2), 46–56.Google Scholar

[100] Gorbachuk, M. L. and Gorbachuk, V. I. 1997. M. G. Krein's Lectures on Entire Operators. Operator Theory: Advances and Applications, vol. 97. Basel: Birkhäuser Verlag.

[101] Hadamard, J. 1892. Essai sur l'étude des fonctions données par leur développement de Taylor. J. Math., 8, 101–186.Google Scholar

[102] Hartmann, A. and Ross, W. T. 2012a. Bad boundary behavior in star-invariant subspaces I. Arkiv for Matematik, 1–22.Google Scholar

[103] Hartmann, A. and Ross, W. T. 2012b. Bad boundary behavior in star invariant subspaces II. Ann. Acad. Sci. Fenn. Math., 37(2), 467–478.Google Scholar

[104] Hartmann, A. and Ross, W. T. 2013. Truncated Toeplitz operators and boundary values in nearly invariant subspaces. Complex Anal. Oper. Theory, 7(1), 261– 273.Google Scholar

[105] Havin, V. and Mashreghi, J. 2003a. Admissible majorants for model subspaces of H2. I. Slow winding of the generating inner function. Canad. J. Math., 55(6), 1231–1263.Google Scholar

[106] Havin, V. and Mashreghi, J. 2003b. Admissible majorants for model subspaces of H2. II. Fast winding of the generating inner function. Canad. J. Math., 55(6), 1264–1301.Google Scholar

[107] Hayashi, E. 1986. The kernel of a Toeplitz operator. Integral Equations Operator Theory, 9(4), 588–591.Google Scholar

[108] Hayashi, E. 1990. Classification of nearly invariant subspaces of the backward shift. Proc. Amer. Math. Soc., 110(2), 441–448.Google Scholar

[109] Hedenmalm, H., Korenblum, B., and Zhu, K. 2000. Theory of Bergman spaces. Graduate Texts in Mathematics, vol. 199. New York: Springer-Verlag.

[110] Helson, H. 1990. Large analytic functions. II. In Analysis and partial differential equations. Lecture Notes in Pure and AppliedMathematics, vol. 122. New York: Dekker, pp. 217–220.

[111] Hitt, D. 1988. Invariant subspaces of H2 of an annulus. Pacific J. Math., 134(1), 101–120.Google Scholar

[112] Hoffman, K. 1962. Banach Spaces of Analytic Functions. Prentice-Hall Series in Modern Analysis. Englewood Cliffs, NJ: Prentice-Hall Inc.

[113] Hrušcev, S.V., and Vinogradov, S.A. 1981. Inner functions and multipliers of Cauchy type integrals. Ark. Mat., 19(1), 23–42.Google Scholar

[114] Inoue, J. 1994. An example of a nonexposed extreme function in the unit ball of H1. Proc. Edinburgh Math. Soc. (2), 37(1), 47–51.Google Scholar

[115] Jung, S., Ko, E., and Lee, J. On scalar extensions and spectral decompositions of complex symmetric operators. J. Math. Anal. Appl. preprint.

[116] Jung, S., Ko, E., Lee, M., and Lee, J. 2011. On local spectral properties of complex symmetric operators. J. Math. Anal. Appl., 379, 325–333.Google Scholar

[117] Kelley, J. L. 1975. General topology. New York-Berlin: Springer-Verlag. Reprint of the 1955 edition [Van Nostrand, Toronto, Ont.], Graduate Texts in Mathematics, No. 27.

[118] Koosis, P. 1998. Introduction to Hp Spaces, 2nd edn. Cambridge Tracts in Mathematics, vol. 115. Cambridge: Cambridge University Press.

[119] Kriete, III, T. L. 1970/71. On the Fourier coefficients of outer functions. Indiana Univ. Math. J., 20, 147–155.Google Scholar

[120] Kriete, III, T. L. 1971. A generalized Paley-Wiener theorem. J. Math. Anal. Appl., 36, 529–555.Google Scholar

[121] Lacey, M. T., Sawyer, E. T., Shen, C.-Y., Uriarte-Tuero, I., and Wick, B. D. Two weight inequalities for the Cauchy transform from R to C+. ArXiv:1310. 4820v2.

[122] Lanucha, B. 2014. Matrix representations of truncated Toeplitz operators. J. Math. Anal. Appl., 413(1), 430–437.Google Scholar

[123] Li, C.G., Zhu, S., and Zhou, T. Foguel operators with complex symmetry. preprint.

[124] Lim, L.-H., and Ye, K. Every matrix is a product of Toeplitz matrices. arXiv:1307.5132v2.

[125] Livsic, M. 1946. On a class of linear operators in Hilbert space. Mat. Sb., 19, 239–262.Google Scholar

[126] Livšic, M. S. 1960. Isometric operators with equal deficiency indices, quasiunitary operators. Amer. Math. Soc. Transl. (2), 13, 85–103.Google Scholar

[127] Lohwater, A. J. and Piranian, G. 1957. The boundary behavior of functions analytic in a disk. Ann. Acad. Sci. Fenn. Ser. A. I., 1957(239), 17.Google Scholar

[128] Lotto, B. A. and McCarthy, J. E. 1993. Composition preserves rigidity. Bull. London Math. Soc., 25(6), 573–576.Google Scholar

[129] Lusin, N. and Priwaloff, J. 1925. Sur l'unicité et la multiplicité des fonctions analytiques. Ann. Sci. école Norm. Sup. (3), 42, 143–191.Google Scholar

[130] Makarov, N. and Poltoratski, A. 2005. Meromorphic inner functions, Toeplitz kernels and the uncertainty principle. In Perspectives in Analysis. Mathematical Physics Studies, vol. 27. Berlin: Springer, pp. 185–252.

[131] Martin, R. T. W. 2010. Symmetric operators and reproducing kernel Hilbert spaces. Complex Anal. Oper. Theory, 4(4), 845–880.Google Scholar

[132] Martin, R. T. W. 2011. Representation of simple symmetric operators with deficiency indices (1, 1) in de Branges space. Complex Anal. Oper. Theory, 5(2), 545–577.Google Scholar

[133] Martin, R. T. W. 2013. Unitary perturbations of compressed n-dimensional shifts. Complex Anal. Oper. Theory, 7(4), 765–799.Google Scholar

[134] Martĺnez-Avendaño, R. A. and Rosenthal, P. 2007. An Introduction to Operators on the Hardy-Hilbert Space. Graduate Texts in Mathematics, vol. 237. New York: Springer.

[135] Mashreghi, J. and Shabankhah, M. 2014. Composition of inner functions. Canad. J. Math., 66(2), 387–399.Google Scholar

[136] Mashreghi, J. 2009. Representation Theorems in Hardy Spaces. London Mathematical Society Student Texts, vol. 74. Cambridge: Cambridge University Press.

[137] Mashreghi, J. 2013. Derivatives of Inner Functions. Fields Institute Monographs, vol. 31. New York: Springer.

[138] Mashreghi, J., and Shabankhah, M. 2013. Composition operators on finite rank model subspaces. Glasg. Math. J., 55(1), 69–83.Google Scholar

[139] Mason, R. C. 1984. Diophantine equations over function fields. London Mathematical Society Lecture Note Series, vol. 96. Cambridge: Cambridge University Press.

[140] Moeller, J. W. 1962. On the spectra of some translation invariant spaces. J. Math. Anal. Appl., 4, 276–296.Google Scholar

[141] Nikolski, N. 1986. Treatise on the Shift Operator. Berlin: Springer-Verlag.

[142] Nikolski, N. 2002a. Operators, Functions, and Systems: An Easy Reading. Vol. 1. Mathematical Surveys and Monographs, vol. 92. Providence, RI: American Mathematical Society. Translated from the French by Andreas Hartmann.

[143] Nikolski, N. 2002b. Operators, Functions, and Systems: An Easy Reading. Vol. 2. Mathematical Surveys and Monographs, vol. 93. Providence, RI: American Mathematical Society. Translated from the French by Andreas Hartmann and revised by the author.

[144] Paulsen, V. 2009. An Introduction to the Theory of Reproducing Kernel Hilbert Spaces. www.math.uh.edu/vern/rkhs.pdf.

[145] Peller, V. V. 1993. Invariant subspaces of Toeplitz operators with piecewise continuous symbols. Proc. Amer. Math. Soc., 119(1), 171–178.Google Scholar

[146] Poltoratski, A. and Sarason, D. 2006. Aleksandrov-Clark measures. In Recent Advances in Operator-related Function Theory. Contemporary Mathematics, vol. 393. Providence, RI: American Mathematical Society, pp. 1–14.

[147] Poltoratski, A. G. 2001. Properties of exposed points in the unit ball of H1. Indiana Univ. Math. J., 50(4), 1789–1806.Google Scholar

[148] Poltoratskii, A. G. 1993. Boundary behavior of pseudocontinuable functions. Algebra i Analiz, 5(2), 189–210.Google Scholar

[149] Privalov, I. I. 1956. Randeigenschaften Analytischer Funktionen. Berlin: VEB Deutscher Verlag der Wissenschaften.

[150] Radjavi, H. and Rosenthal, P. 1973. Invariant Subspaces. Heidelberg: Springer- Verlag.

[151] Richter, S. 1988. Invariant subspaces of the Dirichlet shift. J. Reine Angew. Math., 386, 205–220.Google Scholar

[152] Riesz, F. and Sz.-Nagy, B. 1955. Functional Analysis. New York: Frederick Ungar. Translated by Leo F., Boron.

[153] Rosenblum, M. and Rovnyak, J. 1985. Hardy Classes and Operator Theory. Oxford Mathematical Monographs. New York: The Clarendon Press/Oxford University Press.

[154] Ross, W. T., and Shapiro, H. S. 2002. Generalized Analytic Continuation. University Lecture Series, vol. 25. Providence, RI: American Mathematical Society.

[155] Ross, W. T. 2008. Indestructible Blaschke products. In Banach Spaces of Analytic Functions. Contemporary Mathematics, vol. 454. Providence, RI: American Mathematical Society, pp. 119–134.

[156] Ross, W. T. and Shapiro, H. S. 2003. Prolongations and cyclic vectors. Comput. Methods Funct. Theory, 3(1-2), 453–483.Google Scholar

[157] Royden, H. L. 1988. Real Analysis, 3rd edn. New York: Macmillan.

[158] Rudin, W. 1987. Real and Complex Analysis, 3rd edn. New York: McGraw-Hill.

[159] Rudin, W. 1991. Functional Analysis, 2nd edn. New York: McGraw-Hill.

[160] Saksman, E. 2007. An elementary introduction to Clark measures. Topics in Complex Analysis and Operator Theory.Málaga: University of Málaga, pp. 85–136.

[161] Sarason, D. 1965a. A remark on the Volterra operator. J. Math. Anal. Appl., 12, 244–246.Google Scholar

[162] Sarason, D. 1967. Generalized interpolation in H∞. Trans. Amer. Math. Soc., 127, 179–203.Google Scholar

[163] Sarason, D. 1988. Nearly invariant subspaces of the backward shift. In Contributions to Operator Theory and its Applications (Mesa, AZ, 1987). Operations Theory and Advanced Applications, vol. 35. Basel: Birkhäuser, pp. 481–493.

[164] Sarason, D. 1994a. Kernels of Toeplitz operators. In Toeplitz Operators and Related Topics (Santa Cruz, CA, 1992). Operations Theory Advanced Applications, vol. 71. Basel: Birkhäuser, pp. 153–164.

[165] Sarason, D. 1994b. Sub-Hardy Hilbert Spaces in the Unit Disk. University of Arkansas Lecture Notes in the Mathematical Sciences, 10. New York: John Wiley & Sons.

[166] Sarason, D. 2007. Algebraic properties of truncated Toeplitz operators. Oper. Matrices, 1(4), 491–526.Google Scholar

[167] Sarason, D. 1965b. On spectral sets having connected complement. Acta Sci. Math. (Szeged), 26, 289–299.Google Scholar

[168] Sarason, D. 1989. Exposed points in H1. I. In The Gohberg Anniversary Collection, Vol. II (Calgary, AB, 1988). Operations Theory Advanced Applications, vol. 41. Birkhäuser, Basel, pp. 485–496.

[169] Sedlock, N. 2010. Properties of truncated Toeplitz operators. Ph.D. thesis. ProQuest LLC, Ann Arbor, MI; Washington University in St. Louis.

[170] Sedlock, N. 2011. Algebras of truncated Toeplitz operators. Oper. Matrices, 5(2), 309–326.Google Scholar

[171] Shapiro, H. S. 1964. Weakly invertible elements in certain function spaces, and generators in l1. Michigan Math. J., 11, 161–165.Google Scholar

[172] Shapiro, H. S. 1968. Generalized analytic continuation. In Symposia on Theoretical Physics and Mathematics, Vol. 8 (Symposium, Madras, 1967).New York: Plenum, pp. 151–163.

[173] Shapiro, H. S. 1968/1969. Functions nowhere continuable in a generalized sense. Publ. Ramanujan Inst. No., 1, 179–182.Google Scholar

[174] Shapiro, J. H. 1993. Composition Operators and Classical Function Theory. Universitext: Tracts in Mathematics. New York: Springer-Verlag.

[175] Shimorin, S. 2001. Wold-type decompositions and wandering subspaces for operators close to isometries. J. Reine Angew. Math., 531, 147–189.Google Scholar

[176] Shirokov, N.A. 1978. Ideals and factorization in algebras of analytic functions that are smooth up to the boundary. Trudy Mat. Inst. Steklov., 130, 196–223.Google Scholar

[177] Shirokov, N.A. 1981. Division and multiplication by inner functions in spaces of analytic functions smooth up to the boundary. In Complex Analysis and Spectral Theory (Leningrad, 1979/1980). Lecture Notes inMathematics, vol. 864. Berlin: Springer, pp. 413–439.

[178] Simon, B. 1995. Spectral analysis of rank one perturbations and applications. In Mathematical Quantum Theory. II. Schrödinger Operators (Vancouver, BC, 1993). CRM Proceedings Lecture Notes, vol. 8. Providence, RI: American Mathematical Society, pp. 109–149.

[179] Simon, B. 2005. Orthogonal Polynomials on the Unit Circle.Part 1. American Mathematical Society Colloquium Publications, vol. 54. Providence, RI: American Mathematical Society.

[180] Simon, B. and Wolff, T. 1986. Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians. Comm. Pure Appl. Math., 39(1), 75–90.Google Scholar

[181] Singer, I. 1970. Bases in Banach Spaces. I. New York: Springer-Verlag.

[182] Stegenga, D.A. 1980. Multipliers of the Dirichlet space. Illinois J. Math., 24(1), 113–139.Google Scholar

[183] Stothers, W.W. 1981. Polynomial identities and Hauptmoduln. Quart. J. Math. Oxford Ser. (2), 32(127), 349–370.Google Scholar

[184] Sz.-Nagy, B. 1953. Sur les contractions de l'espace de Hilbert. Acta Sci. Math. Szeged, 15, 87–92.Google Scholar

[185] Sz.-Nagy, B. and Foiaş, C. 1968. Dilatation des commutants d'opérateurs. C. R. Acad. Sci. Paris Sér. A-B, 266, A493–A495.Google Scholar

[186] Sz.-Nagy, B., Foias, C., Bercovici, H., and Kérchy, L. 2010. Harmonic Analysis of Operators on Hilbert Space, 2nd edn. Universitext. New York: Springer.

[187] Takenaka, S. 1925. On the orthonormal functions and a new formula of interpolation. Jap. J. Math., 2, 129–145.Google Scholar

[188] Teschl, G. 2009. Mathematical methods in quantum mechanics. Graduate Studies in Mathematics, vol. 99. Providence, RI: American Mathematical Society.

[189] Vol'berg, A. L. 1981. Thin and thick families of rational fractions. In Complex Analysis and Spectral Theory (Leningrad, 1979/1980). Lecture Notes in Mathematics, vol. 864. Berlin: Springer, pp. 440–480.

[190] Vol'berg, A. L., and Treil', S.R. 1986. Embedding theorems for invariant subspaces of the inverse shift operator. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 149(XV), 38–51, 186–187.Google Scholar

[191] Wang, X. and Gao, Z. 2009. A note on Aluthge transforms of complex symmetric operators and applications. Integral Equations Operator Theory, 65(4), 573–580.Google Scholar

[192] Wang, X. and Gao, Z. 2010. Some equivalence properties of complex symmetric operators. Math. Pract. Theory, 40(8), 233–236.Google Scholar

[193] Yabuta, K. 1971. Remarks on extremum problems in H1. Tôhoku Math. J. (2), 23, 129–137.Google Scholar

[194] Zagorodnyuk, S. M. 2010. On a J-polar decomposition of a bounded operator and matrix representations of J-symmetric, J-skew-symmetric operators. Banach J. Math. Anal., 4(2), 11–36.Google Scholar

[195] Zhu, S. and Li, C. G. 2013. Complex symmetric weighted shifts. Trans. Amer. Math. Soc., 365(1), 511–530.Google Scholar

[196] Zhu, S., Li, C. G., and Ji, Y.Q. 2012. The class of complex symmetric operators is not norm closed. Proc. Amer. Math. Soc., 140(5), 1705–1708.Google Scholar