Orthogonal Polynomials On The Unit Circle

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Orthogonal Polynomials On The Unit Circle

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Author : Barry Simon
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

Orthogonal Polynomials On The Unit Circle written by Barry Simon and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Education categories.

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

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Author : Barry Simon
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-08-05

Orthogonal Polynomials On The Unit Circle written by Barry Simon and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-05 with Mathematics categories.

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 Spectral Theory

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Author : Barry Simon
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

Orthogonal Polynomials On The Unit Circle Spectral Theory written by Barry Simon and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Science categories.

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

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Author :
language : en
Publisher:
Release Date : 1994

Orthogonal Polynomials On The Unit Circle written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Orthogonal polynomials categories.

Classical And Quantum Orthogonal Polynomials In One Variable

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Author : Mourad Ismail
language : en
Publisher: Cambridge University Press
Release Date : 2005-11-21

Classical And Quantum Orthogonal Polynomials In One Variable written by Mourad Ismail and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-21 with Mathematics categories.

The first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback.

Orthogonal Rational Functions

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Author : Adhemar Bultheel
language : en
Publisher: Cambridge University Press
Release Date : 1999-02-13

Orthogonal Rational Functions written by Adhemar Bultheel and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-02-13 with Mathematics categories.

This book generalises the classical theory of orthogonal polynomials on the complex unit circle, or on the real line to orthogonal rational functions whose poles are among a prescribed set of complex numbers. The first part treats the case where these poles are all outside the unit disk or in the lower half plane. Classical topics such as recurrence relations, numerical quadrature, interpolation properties, Favard theorems, convergence, asymptotics, and moment problems are generalised and treated in detail. The same topics are discussed for the different situation where the poles are located on the unit circle or on the extended real line. In the last chapter, several applications are mentioned including linear prediction, Pisarenko modelling, lossless inverse scattering, and network synthesis. This theory has many applications in theoretical real and complex analysis, approximation theory, numerical analysis, system theory, and in electrical engineering.

Orthogonal Polynomials And Their Applications

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Author : Jaime Vinuesa
language : en
Publisher: CRC Press
Release Date : 1989-05-25

Orthogonal Polynomials And Their Applications written by Jaime Vinuesa and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-05-25 with Mathematics categories.

Orthogonal Polynomials And Painlev Equations

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Author : Walter Van Assche
language : en
Publisher: Cambridge University Press
Release Date : 2018

Orthogonal Polynomials And Painlev Equations written by Walter Van Assche and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Mathematics categories.

There are a number of intriguing connections between Painlev equations and orthogonal polynomials, and this book is one of the first to provide an introduction to these. Researchers in integrable systems and non-linear equations will find the many explicit examples where Painlev equations appear in mathematical analysis very useful. Those interested in the asymptotic behavior of orthogonal polynomials will also find the description of Painlev transcendants and their use for local analysis near certain critical points helpful to their work. Rational solutions and special function solutions of Painlev equations are worked out in detail, with a survey of recent results and an outline of their close relationship with orthogonal polynomials. Exercises throughout the book help the reader to get to grips with the material. The author is a leading authority on orthogonal polynomials, giving this work a unique perspective on Painlev equations.

Difference Equations Special Functions And Orthogonal Polynomials

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Author : Saber Elaydi
language : en
Publisher: World Scientific
Release Date : 2007

Difference Equations Special Functions And Orthogonal Polynomials written by Saber Elaydi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Science categories.

This volume contains talks given at a joint meeting of three communities working in the fields of difference equations, special functions and applications (ISDE, OPSFA, and SIDE). The articles reflect the diversity of the topics in the meeting but have difference equations as common thread. Articles cover topics in difference equations, discrete dynamical systems, special functions, orthogonal polynomials, symmetries, and integrable difference equations.

Difference Equations Special Functions And Orthogonal Polynomials Proceedings Of The International Conference

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Author : Jim M Cushing
language : en
Publisher: World Scientific
Release Date : 2007-05-21

Difference Equations Special Functions And Orthogonal Polynomials Proceedings Of The International Conference written by Jim M Cushing and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-21 with Mathematics categories.

This volume contains talks given at a joint meeting of three communities working in the fields of difference equations, special functions and applications (ISDE, OPSFA, and SIDE). The articles reflect the diversity of the topics in the meeting but have difference equations as common thread. Articles cover topics in difference equations, discrete dynamical systems, special functions, orthogonal polynomials, symmetries, and integrable difference equations.