Orthogonal Functions

Moment Theory and Continued Fractions
1. Auflage 1998
ISBN: 978-0-8247-0207-6
Verlag: CRC Press

Buch, Englisch, 438 Seiten, Format (B × H): 178 mm x 254 mm, Gewicht: 822 g

Reihe: Lecture Notes in Pure and Applied Mathematics

"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."

Autoren/Hrsg.

Jones, William

Ranga, A. Sri

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

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.

Über Autor(innen)

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.