Orthogonal Polynomials on the Unit Circle: Spectral theory
Title | Orthogonal Polynomials on the Unit Circle: Spectral theory PDF eBook |
Author | Barry Simon |
Publisher | American Mathematical Soc. |
Pages | 608 |
Release | 2005 |
Genre | Mathematics |
ISBN | 9780821836750 |
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 on the Unit Circle
Title | Orthogonal Polynomials on the Unit Circle PDF eBook |
Author | Barry Simon |
Publisher | American Mathematical Soc. |
Pages | 610 |
Release | 2005 |
Genre | Education |
ISBN | 082184864X |
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.
Orthogonal Polynomials on the Unit Circle
Title | Orthogonal Polynomials on the Unit Circle PDF eBook |
Author | Barry Simon |
Publisher | American Mathematical Soc. |
Pages | 498 |
Release | 2009-08-05 |
Genre | Mathematics |
ISBN | 0821848631 |
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 on the Unit Circle
Title | Orthogonal Polynomials on the Unit Circle PDF eBook |
Author | Barry Simon |
Publisher | |
Pages | 1044 |
Release | 2005 |
Genre | Orthogonal polynomials |
ISBN | 9781470431990 |
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 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 po.
Orthogonal Polynomials on the Unit Circle
Title | Orthogonal Polynomials on the Unit Circle PDF eBook |
Author | |
Publisher | |
Pages | 220 |
Release | 1994 |
Genre | Orthogonal polynomials |
ISBN |
Zeros of Random Orthogonal Polynomials on the Unit Circle
Title | Zeros of Random Orthogonal Polynomials on the Unit Circle PDF eBook |
Author | Mihai Stoiciu |
Publisher | |
Pages | 182 |
Release | 2005 |
Genre | Electronic dissertations |
ISBN |
Orthogonal Polynomials
Title | Orthogonal Polynomials PDF eBook |
Author | Gabor Szeg |
Publisher | American Mathematical Soc. |
Pages | 448 |
Release | 1939-12-31 |
Genre | Mathematics |
ISBN | 0821810235 |
The general theory of orthogonal polynomials was developed in the late 19th century from a study of continued fractions by P. L. Chebyshev, even though special cases were introduced earlier by Legendre, Hermite, Jacobi, Laguerre, and Chebyshev himself. It was further developed by A. A. Markov, T. J. Stieltjes, and many other mathematicians. The book by Szego, originally published in 1939, is the first monograph devoted to the theory of orthogonal polynomials and its applications in many areas, including analysis, differential equations, probability and mathematical physics. Even after all the years that have passed since the book first appeared, and with many other books on the subject published since then, this classic monograph by Szego remains an indispensable resource both as a textbook and as a reference book. It can be recommended to anyone who wants to be acquainted with this central topic of mathematical analysis.