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E-raamat: Bounds and Asymptotics for Orthogonal Polynomials for Varying Weights

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  • Formaat: PDF+DRM
  • Sari: SpringerBriefs in Mathematics
  • Ilmumisaeg: 13-Feb-2018
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319729473
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Bounds and Asymptotics for Orthogonal Polynomials for Varying WeightsSuurem pilt
  • Formaat: PDF+DRM
  • Sari: SpringerBriefs in Mathematics
  • Ilmumisaeg: 13-Feb-2018
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319729473
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This book establishes bounds and asymptotics under almost minimal conditions on the varying weights, and applies them to universality limits and entropy integrals. Orthogonal polynomials associated with varying weights play a key role in analyzing random matrices and other topics.

This book will be of use to a wide community of mathematicians, physicists, and statisticians dealing with techniques of potential theory, orthogonal polynomials, approximation theory, as well as random matrices.

Arvustused

This book is written by two well-reputed specialists on orthogonal polynomials. Thus, It will be of great interest to those studying orthogonal polynomials, as well as Ph.D. students specializing in this or related areas. The structure of the text is nice. In fifteen short chapters the authors provide us with the statement of the results and their corresponding proofs in a rigorous and precise way. (Juan José Monero-Balcázar, Mathematical Reviews, October, 2018)

1 Introduction
1(8)
2 Statement of Main Results
9(4)
3 Potential Theoretic Estimates
13(16)
4 Restricted Range Inequalities
29(8)
5 Bounds for Christoffel Functions
37(10)
6 Spacing of Zeros
47(6)
7 Bounds on Orthogonal Polynomials
53(10)
8 Markov-Bernstein Inequalities in L∞
63(4)
9 Discretization of Potentials
67(16)
10 Derivatives of Discretized Polynomials
83(10)
11 Weighted Polynomial Approximations
93(24)
12 Formulae Involving Bernstein-Szego Polynomials
117(6)
13 Asymptotics of Orthonormal Polynomials
123(20)
14 Further Bounds
143(10)
15 Universality Limits and Entropy Integrals
153(12)
References 165(4)
Index 169
Eli Levin is an emeritus professor at the Open University of Israel in Ramat Aviv.  Doron Lubinsky is a professor at Georgia Institute of Technology. Both are authors of papers on approximation theory, and a joint monograph on orthogonal polynomials.
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