Orthogonal Functions: Moment Theory and Continued Fractions

ISBN-13: 9780824702076 / Angielski / Miękka / 1998 / 438 str.

A. Sri Ranga; Jones Jones; Jr. William B. Jones

Opis

"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."

Spis treści

Chebyshev-Laurent polynomials and weighted approximation; natural solutions of indeterminate strong Stieltjes moment problems derived from PC-fractions; a class of indeterminate strong Stieltjes moment problems with discrete distributions; symmetric orthogonal L-polynomials in the complex plane; continued fractions and orthogonal rational functions; interpolation of Nevanlinna functions by rationals with poles on the real line; symmetric orthogonal Laurent polynomials; interpolating Laurent polynomials; computation of the gamma and Binet functions by Stieltjes continued fractions; formulas for the moments of some strong moment distributions; orthogonal Laurent polynomials of Jacobi, Hermite and Laguerre types; regular strong Hamburger moment problems; asymptotic behaviour of the continued fraction coefficients of a class of Stieltjes transforms, including the Binet function; uniformity and speed of convergence of complex continued fractions K(an/1); separation theorem of Chebyshev-Markov-Stieltjes type for Laurent polynomials orthogonal on (0, alpha); orthogonal polynomials associated with a non-diagonal Sobolev inner product with polynomial coefficients; remarks on canonical solutions of strong moment problems; Sobolev orthogonality and properties of the generalized Laguerre polynomials; a combination of two methods in frequency analysis -the R(N)-process; zeros of Szego polynomials used in frequency analysis; some probabilistic remarks on the boundary version of Worpitzky's theorem.

O autorze

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.