Author: I͡A. L. GeronimusPublisher:
ISBN:
Category : Functions, Orthogonal
Languages : en
Pages : 84
Book Description
Polynomials Orthogonal on a Circle and Their Applications
Author: I͡A. L. GeronimusPublisher:
ISBN:
Category : Functions, Orthogonal
Languages : en
Pages : 84
Book Description
Orthogonal Polynomials on the Unit Circle
Author: Barry SimonPublisher: American Mathematical Soc.
ISBN: 0821848631
Category : Mathematics
Languages : en
Pages : 466
Book Description
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.
Polynomials orthogonal on a circle and their applications
Author: Jakov L. GeronimusOrthogonal Polynomials on the Unit Circle
Author: Barry SimonPublisher: American Mathematical Soc.
ISBN: 082184864X
Category : Education
Languages : en
Pages : 610
Book Description
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
Author: Publisher:
ISBN:
Category : Orthogonal polynomials
Languages : en
Pages : 220
Book Description
Classical and Quantum Orthogonal Polynomials in One Variable
Author: Mourad IsmailPublisher: Cambridge University Press
ISBN: 9780521782012
Category : Mathematics
Languages : en
Pages : 748
Book Description
The first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback.
Orthogonal Polynomials on the Unit Circle: Spectral theory
Author: Barry SimonPublisher: American Mathematical Soc.
ISBN: 9780821836750
Category : Mathematics
Languages : en
Pages : 608
Book Description
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
Author: Gabor SzegPublisher: American Mathematical Soc.
ISBN: 0821810235
Category : Mathematics
Languages : en
Pages : 432
Book Description
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.
Orthogonal Polynomials and Their Applications
Author: Jaime VinuesaPublisher: CRC Press
ISBN: 9780824781613
Category : Mathematics
Languages : en
Pages : 238
Book Description
Orthogonal Polynomials and their Applications
Author: Manuel AlfaroPublisher: Springer
ISBN: 3540392955
Category : Mathematics
Languages : en
Pages : 351
Book Description
The Segovia meeting set out to stimulate an intensive exchange of ideas between experts in the area of orthogonal polynomials and its applications, to present recent research results and to reinforce the scientific and human relations among the increasingly international community working in orthogonal polynomials. This volume contains original research papers as well as survey papers about fundamental questions in the field (Nevai, Rakhmanov & López) and its relationship with other fields such as group theory (Koornwinder), Padé approximation (Brezinski), differential equations (Krall, Littlejohn) and numerical methods (Rivlin).