Orthogonal Polynomials on the Unit Circle
Orthogonal Polynomials on the Unit Circle

Author: Barry Simon

Publisher: American Mathematical Soc.

Published: 2009-08-05

Total Pages: 498

ISBN-13: 0821848631

DOWNLOAD EBOOK

This two-part book is a comprehensive overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. A major theme involves the connections between the Verblunsky coefficients (the coefficients of the recurrence equation for the orthogonal polynomials) and the measures, an analog of the spectral theory of one-dimensional Schrodinger operators. Among the topics discussed along the way are the asymptotics of Toeplitz determinants (Szego's theorems), limit theorems for the density of the zeros of orthogonal polynomials, matrix representations for multiplication by $z$ (CMV matrices), periodic Verblunsky coefficients from the point of view of meromorphic functions on hyperelliptic surfaces, and connections between the theories of orthogonal polynomials on the unit circle and on the real line.

Orthogonal Polynomials
Orthogonal Polynomials

Author: Paul G. Nevai

Publisher: American Mathematical Soc.

Published: 1979

Total Pages: 196

ISBN-13: 0821822136

DOWNLOAD EBOOK

The purpose of the present paper is to improve some results on orthogonal polynomials, Christoffel functions, orthogonal Fourier series, eigenvalues of Toeplitz matrices and Lagrange interpolation. Most of the paper deals with Christoffel functions and their applications.

Orthogonal Polynomials on the Unit Circle: Spectral theory
Orthogonal Polynomials on the Unit Circle: Spectral theory

Author: Barry Simon

Publisher: American Mathematical Soc.

Published: 2005

Total Pages: 608

ISBN-13: 9780821836750

DOWNLOAD EBOOK

Presents an overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. This book discusses topics such as asymptotics of Toeplitz determinants (Szego's theorems), and limit theorems for the density of the zeros of orthogonal polynomials.

Orthogonal Polynomials
Orthogonal Polynomials

Author: Gábor Szegő

Publisher: American Mathematical Soc.

Published: 1975

Total Pages: 456

ISBN-13:

DOWNLOAD EBOOK

Part of ""Colloquium Series"", this book presents systematic treatment of orthogonal polynomials.

Orthogonal Polynomials
Orthogonal Polynomials

Author: Géza Freud

Publisher: Elsevier

Published: 2014-05-17

Total Pages: 295

ISBN-13: 148315940X

DOWNLOAD EBOOK

Orthogonal Polynomials contains an up-to-date survey of the general theory of orthogonal polynomials. It deals with the problem of polynomials and reveals that the sequence of these polynomials forms an orthogonal system with respect to a non-negative m-distribution defined on the real numerical axis. Comprised of five chapters, the book begins with the fundamental properties of orthogonal polynomials. After discussing the momentum problem, it then explains the quadrature procedure, the convergence theory, and G. Szego's theory. This book is useful for those who intend to use it as reference for future studies or as a textbook for lecture purposes

Orthogonal Polynomials on the Unit Circle
Orthogonal Polynomials on the Unit Circle

Author: Barry Simon

Publisher: American Mathematical Soc.

Published: 2005

Total Pages: 610

ISBN-13: 082184864X

DOWNLOAD EBOOK

This two-part volume gives a comprehensive overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. A major theme involves the connections between the Verblunsky coefficients (the coefficients of the recurrence equation for the orthogonal polynomials) and the measures, an analog of the spectral theory of one-dimensional Schrödinger operators. Among the topics discussed along the way are the asymptotics of Toeplitz determinants (Szegő's theorems), limit theorems for the density of the zeros of orthogonal polynomials, matrix representations for multiplication by (CMV matrices), periodic Verblunsky coefficients from the point of view of meromorphic functions on hyperelliptic surfaces, and connections between the theories of orthogonal polynomials on the unit circle and on the real line. The book is suitable for graduate students and researchers interested in analysis.