Boundary Asymptotics For Orthogonal Rational Functions On The Unit Circle
Download Boundary Asymptotics For Orthogonal Rational Functions On The Unit Circle full books in PDF, epub, and Kindle. Read online free Boundary Asymptotics For Orthogonal Rational Functions On The Unit Circle ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
| Author | : Adhemar Bultheel |
| Publisher | : Cambridge University Press |
| Total Pages | : 423 |
| Release | : 1999-02-13 |
| Genre | : Mathematics |
| ISBN | : 0521650062 |
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.
| Author | : Barry Simon |
| Publisher | : American Mathematical Soc. |
| Total 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.
| Author | : Barry Simon |
| Publisher | : American Mathematical Soc. |
| Total 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.
| Author | : Atkinson |
| Publisher | : Academic Press |
| Total Pages | : 586 |
| Release | : 1964-01-01 |
| Genre | : Computers |
| ISBN | : 0080955169 |
Discrete and Continuous Boundary Problems
| Author | : |
| Publisher | : |
| Total Pages | : 456 |
| Release | : 2002 |
| Genre | : Continued fractions |
| ISBN | : |
| Author | : |
| Publisher | : |
| Total Pages | : 1208 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Heinrich G. W. Begehr |
| Publisher | : World Scientific |
| Total Pages | : 1497 |
| Release | : 2009 |
| Genre | : Mathematics |
| ISBN | : 9812835628 |
International ISAAC (International Society for Analysis, its Applications and Computation) Congresses have been held every second year since 1997. The proceedings report on a regular basis on the progresses of the field in recent years, where the most active areas in analysis, its applications and computation are covered. Plenary lectures also highlight recent results. This volume concentrates mainly on partial differential equations, but also includes function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, stochastic analysis, inverse problems, homogenization, continuum mechanics, mathematical biology and medicine. With over 350 participants attending the congress, the book comprises 140 papers from 211 authors. The volume also serves for transferring personal information about the ISAAC and its members. This volume includes citations for O Besov, V Burenkov and R P Gilbert on the occasion of their anniversaries.
| Author | : |
| Publisher | : World Scientific |
| Total Pages | : 1497 |
| Release | : 2009-05-12 |
| Genre | : Mathematics |
| ISBN | : 9812835636 |
International ISAAC (International Society for Analysis, its Applications and Computation) Congresses have been held every second year since 1997. The proceedings report on a regular basis on the progresses of the field in recent years, where the most active areas in analysis, its applications and computation are covered. Plenary lectures also highlight recent results. This volume concentrates mainly on partial differential equations, but also includes function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, stochastic analysis, inverse problems, homogenization, continuum mechanics, mathematical biology and medicine. With over 350 participants attending the congress, the book comprises 140 papers from 211 authors. The volume also serves for transferring personal information about the ISAAC and its members. This volume includes citations for O. Besov, V. Burenkov and R.P. Gilbert on the occasion of their anniversaries.
| Author | : Jorge ArvesĂș |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 314 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 0821848038 |
This volume contains invited lectures and selected contributions from the International Workshop on Orthogonal Polynomials and Approximation Theory, held at Universidad Carlos III de Madrid on September 8-12, 2008, and which honored Guillermo Lopez Lagomasino on his 60th birthday. This book presents the state of the art in the theory of Orthogonal Polynomials and Rational Approximation with a special emphasis on their applications in random matrices, integrable systems, and numerical quadrature. New results and methods are presented in the papers as well as a careful choice of open problems, which can foster interest in research in these mathematical areas. This volume also includes a brief account of the scientific contributions by Guillermo Lopez Lagomasino.
| Author | : Gabor Szeg |
| Publisher | : American Mathematical Soc. |
| Total 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.
