Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-24T01:44:25.931Z Has data issue: false hasContentIssue false
  • English
  • Français

Convergence of Fourier–Padé Approximants for Stieltjes Functions

Published online by Cambridge University Press:  20 November 2018

M. Bello Hernández  and
J. Mínguez Ceniceros
M. Bello Hernández
Affiliation:
Dpto. de Matemáticas y Computación, Universidad de La Rioja, Edificio J. L. Vives, Luis de Ulloa, s/n, 26004 Logroño Spain e-mail: [email protected]@dmc.unirioja.es
J. Mínguez Ceniceros
Affiliation:
Dpto. de Matemáticas y Computación, Universidad de La Rioja, Edificio J. L. Vives, Luis de Ulloa, s/n, 26004 Logroño Spain e-mail: [email protected]@dmc.unirioja.es
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We prove convergence of diagonal multipoint Padé approximants of Stieltjes-type functions when a certain moment problem is determinate. This is used for the study of the convergence of Fourier–Padé and nonlinear Fourier–Padé approximants for such type of functions.

Keywords

41A2041A2144A60Rational approximationmultipoint Padé approximantsFourier—Padé approximantsmoment problem
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 58 , Issue 2 , 01 April 2006 , pp. 249 - 261
Copyright
Copyright © Canadian Mathematical Society 2006

References

[1] Akhiezer, N. I. The Classical Moment Problem and Some Related Questions in Analysis. Ungar, New York, 1956.Google Scholar
[2] Baker, G. A. Jr. and Graves-Morris, P., Padé Approximants, II. Encyclopedia of Mathematics and Its Applications 14, Cambridge University Press, Cambridge, 1981.Google Scholar
[3] Folland, G. B. Real Analysis: Modern Techniques and Their Applications. John Wiley, New York, 1984.Google Scholar
[4] Gonchar, A. A. and López Lagomasino, G., Markov's theorem for multipoint Padé approximants. (Russian) Mat. Sb (N. S.) 105(147)(1978), no. 4, 512–524; English transl. Math. USSR-Sb. 34(1978), no. 4, 449–459.Google Scholar
[5] Gonchar, A. A. and Rakhmanov, E. A. Equilibrium distributions and the rate of rational approximation of analytic functions. (Russian) Mat. Sb. (N. S.) 134(176)(1987), no. 3, 306–352; English transl. Math. USSR-Sb. 62(1989), no. 2, 305–348.Google Scholar
[6] Gonchar, A. A. Rakhamanov, E. A. and Suetin, S. P. On the rate of convergence of Padé approximants of orthogonal expansions. Progress in Approximation Theory, Springer Ser. Comput. Math., 19, Springer, New York, 1992, pp. 169–190.Google Scholar
[7] Jones, W. B. Thron, W. J. and Waadeland, H., A strong Stieltjes moment problem. Trans. Amer. Math. Soc. 261(1980), no. 2, 503–528.Google Scholar
[8] López Lagomasino, G., Conditions for convergence of multipoint Padé approximants for functions of Stieltjes type. (Russian) Mat. Sb. (N. S.) 107(149)(1978), no. 1, 69–83; English transl. Math. USSR-Sb. 35(1979), no. 3, 363–376.Google Scholar
[9] Nikishin, E. M. and Sorokin, V. N. Rational approximations and orthogonality. Translations of Mathematical Monographs 92, American Mathematical Society, Providence, RI, 1991.Google Scholar
[10] Rudin, W., Real and Complex Analysis. McGraw-Hill, New York, 1966.Google Scholar
[11] Schechter, E., Handbook of Analysis and Its Foundations. Academic Press, San Diego, CA, 1997.Google Scholar
[12] Stahl, H. and Totik, V., General Orthogonal Polynomials. Encyclopedia of Mathematics and Its Applications 43, Cambridge University Press, Cambridge, 1992.Google Scholar
[13] Szegőo, G., Orthogonal polynomials. Fourth edition. American Mathematical Society Colloquium Publications 23, American Mathematical Society, Providence, RI, 1975.Google Scholar