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The Operator Theory of Generalized Boundary Value Problems

Published online by Cambridge University Press:  20 November 2018

R. C. Brown
R. C. Brown*
Affiliation:
University of Wisconsin, Madison, Wisconsin
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In this paper we develop a theory of maximal and minimal operators and their duals associated with the system

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 3 , 01 June 1976 , pp. 486 - 512
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Akhiezer, N. I., The calculus of variations (Blaisdell, New York, 1962).Google Scholar
2. Arens, R., Operational calculus of linear relations, Pacific J. Math. 11 (1961), 9–23.Google Scholar
3. Coddington, E. A., Self-adjoint problems for nondensely defined ordinary differential operators and their eigenfunction expansions, Advances in Math. 15 (1975), 1–40.Google Scholar
4. Brown, R. C., Duality theory for nth. order differential operators under Stieltjes boundary conditions, SIAM J. Math. Anal. 6 (1975), 882–900.Google Scholar
5. Brown, R. C., Duality theory for nth. order differential operators under Stieltjes boundary conditions, II: non-sm∞th coefficients and non-singular measures, Ann. Mat. Pura Appl. 105 (1975), 141–170.Google Scholar
6. Brown, R. C., (yt Adjoint domains and generalized splines, Czechoslovak Math. J. 25 (1975), 134–137.Google Scholar
7. Dunford, N. and Schwartz, J., Linear operators, part I (Interscience, New York, 1957).Google Scholar
8. Goldberg, S., Unbounded linear operators (McGraw-Hill, New York, 1966).Google Scholar
9. Golomb, M. and Jerome, J., Linear ordinary differential equations with boundary conditions on arbitrary point sets, Trans. Amer. Math. Soc. 153 (1971), 235–264.Google Scholar
10. Jerome, J. W. and Schumaker, L. L., On Lg-splines, J. Approximation Theory 2 (1969), 29–49.Google Scholar
11. Kelley, J. L. and Namioka, I., Linear topological spaces (Van Nostrand, Princeton, New Jersey, 1963).Google Scholar
12. Kim, T., Investigation of a differential-boundary operator of the second order with an integral boundary condition on a semi-axis, J. Math. Anal. Appl. 44 (1973), 434–446.Google Scholar
13. Krall, A. M., A non-homogenous eigenfunction expansion, Trans. Amer. Math. Soc. 117 (1965), 352–361.Google Scholar
14. Krall, A. M., The adjoint of a differential operator with integral boundary conditions, Proc. Amer. Math. Soc. 16 (1965), 738–742.Google Scholar
15. Krall, A. M., The development of general differential and general differential-boundary systems, Rocky Mountain J. Math. 5 (1975), 493–542.Google Scholar
16. Naimark, M. A., Investigation of the spectrum and expansion in eigenfunctions of a nonselfadjoint differential operator of second order on a semi-axis, Trudy Moskov. Mat. Obsc. 3 (1954), 181-270; Amer. Math. Soc. Transi. 16 (1960), 103–194.Google Scholar
17. Naimark, M. A., Linear differential operators, part II (Ungar, New York, 1968).Google Scholar
18. Yosida, K., Functional analysis (Academic Press, New York, 1965).Google Scholar