Orthogonal Functions: Moment Theory and Continued Fractions

by William Jones (Editor)

Overview

"Oulines an array of recent work on the analytic theory and potential applications of continued fractions, linear functionals, orthogonal functions, moment theory, and integral transforms. Describes links between continued fractions. Pade approximation, special functions, and Gaussian quadrature."

Product Details

ISBN-13:	9781138413269
Publisher:	Taylor & Francis
Publication date:	08/02/2017
Series:	Lecture Notes in Pure and Applied Mathematics
Pages:	440
Product dimensions:	7.00(w) x 10.00(h) x (d)

About the Author

WILLIAM B. JONES is Professor Emeritus of Mathematics at the University of Colo­rado. He is the author or coauthor of more than 190 research papers, abstracts, and invited lectures. Dr. Jones is a member of the American Mathematical Society, the Mathematical Association of America, the Society for Industrial and Applied Mathematics, and the American Association of University Professors. He received the B.A. degree (1953) from Jacksonville State University, Alabama, and the M.A. (1955) and Ph.D. (1963) degrees from Vanderbilt University, Nashville, Tennessee. A. SRI RANGA is Professor of Numerical Analysis in the Departamento de Ciencias de Computa;:ao e Estatfstica, Instituto de Biociencias, Letras e Ciencias Exatas, Universidade Estadual Paulista, in Sao Jose do Rio Preto, Sao Paulo, Brazil. He is a member of the Sociedade Brasileira de Matematica Aplicada e Computacinal and the American Mathematical Society. Dr. Sri Ranga received the Ph.D. degree (1984) from the University of St. Andrews, Scotland, and the Livre Docencia degree (1991) from the Universidade de Sao Paulo, in Sao Carlos, Sao Paulo, Brazil.

Table of Contents

Preface — Contributors — Participants — 1. Chebyshev-Laurent Polynomials and Weighted Approximation Eliana /X. L. de Andrade and Dimitar K. Dimitrov — 2. Natural Solutions of Indeterminate Strong Stieltjes Moment Problems Derived from PC-Fractions Catherine M. Bonan-Hamada, William B. Jones, and Olav Njastad — 3. A Class oflndeterminate Strong Stieltjes Moment Problems with Discrete Distributions Catherine M. Bonan-Hamada, William B. Jones, Olav Njastad, and W. J. Thran — 4. Symmetric Orthogonal L-Polynomials in the Complex Plane /C. F. Bracciali, J. M. V. Cape /a, and A. Sri Ranga — 5. Continued Fractions and Orthogonal Rational Functions Adhemar Bu thee!, Pablo Gonzalez-Vera, Erik Hendriksen, and Olav Njastad — 6. Interpolation of Nevanlinna Functions by Rationals with Poles on the Ral Line /Adhemar Bultheel, Pablo Gonzalez-Vera, Erik Hendriksen, and Olav Njastad — 7. Symmetric Orthogonal Laurent Polynomials /Lyle Cochran and S. Clement Cooper — 8. Interpolating Laurent Polynomials /S. Clement Cooper and Philip E. Gustafson — 9. Computation of the Binet and Gamma Functions by Stieltjes Continued Fractions /Cathleen M. Craviotto, William B. Jones, and Nancy J. Wyshinski — 10. Formulas for the Moments of Some Strong Moment Distributions Brian A. Hagler — 11. Orthogonal Laurent Polynomials of Jacobi, Hermite, and Laguerre Types Brian A. Hagler, William B. Jones, and W. J. Thron — 12. Regular Strong Hamburger Moment Problems William B. Jones and Guoxiang Shen — 13. Asymptotic Behavior of the Continued Fraction Coefficients of a Class of Stieltjes Transforms Including the Binet Function William B. Jones and Walter Van Assche — 14. Uniformity and Speed of Convergence of Complex Continued Fractions K(a /1 /L. J. Lange — 15. Separation Theorem of Chebyshev-Markov-Stieltjes Type for Laurent Polynomials Orthogonal on (0, oo) /XinLi — 16. Orthogonal Polynomials Associated with a Nondiagonal Sobolev Inner Product with Polynomial Coefficients Maria Alvarez de Morales, Teresa E. Perez, Miguel A. Piiiar, and Andre Ronveaux — 17. Remarks on Canonical Solutions of Strong Moment Problems /Olav Njastad — 18. Sobolev Orthogonality and Properties of the Generalized Laguerre Polynomials Teresa E. Perez and Miguel A. Piiiar — 19. A Combination of Two Methods in Frequency Analysis: The R(N)-Process /Vigdis Petersen — 20. Zeros of Szego Polynomials Used in Frequency Analysis /Vigdis Petersen — 21. Some Probabilistic Remarks on the Boundary Version of Worpitzky's Theorem /Haakon Waadeland.