Asymptotics for orthogonal polynomials:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1987
|
| Series: | Lecture notes in mathematics
1265 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. [181] - 195 |
| Physical Description: | VI, 201 S. graph. Darst. |
| ISBN: | 3540180230 0387180230 |
Staff View
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Record in the Search Index
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| adam_text | TABLE OF CONTENTS
Introduction
O.I Definitions and examples 1
0.2 General properties 7
0.3 Outline of this monograph 11
0.4 A short historical note 12
Chapter 1 : Orthogonal Polynomials on a Compact Set
1.1 Some notions from potential theory 14
1.2 Main theorem 18
1.3 Orthogonal polynomials on [ 1,1] 24
1.3.1 The Szegb class 25
1.3.2 Beyond the Szegb class 33
1.4 Orthogonal polynomials on Julia sets 35
Chapter 2 : Asymptotically Periodic Recurrence Coefficients
2.1 Periodic recurrence coefficients 43
2.2 Asymptotic periodicity 53
2.3 Construction of the spectral measure 63
2.4 Strong asymptotics 70
2.5 Weak asymptotics 74
2.6 Periodicity of period N=l 81
Chapter 3 : Probabilistic Proofs of Asymptotic Formulas
3.1 The local limit theorem in probability theory 87
3.2 First order results 90
3.3 Asymptotic expansions 100
Chapter 4 : Orthogonal Polynomials on Unbounded Sets
4.1 Contracted zero distributions 105
4.2 Freud conjectures 112
4.3 Results using the recurrence relation 115
4.4 Plancherel Rotach asymptotics 124
4.5 Weighted zero distributions 128
VI
4.6 Rate of convergence for weighted zero distributions 132
Chapter 5 : Zero Distribution and Consequences
5.1 Asymptotic behaviour of the Taylor coefficients 138
5.2 Weak asymptotics for Christoffel functions 151
5.3 Toeplitz matrices associated with orthogonal polynomials 154
5.4 Functions of the second kind 159
Chapter 6 : Some applications
6.1 Random matrices 164
6.2 Discrete Schrodinger equations 168
6.3 Birth and death processes 171
Appendix
A.I The Stieltjes transform 175
A.2 The Stieltjes convolution 177
References 181
Subject Index 196
|
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| indexdate | 2024-07-09T15:17:38Z |
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| isbn | 3540180230 0387180230 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000422084 |
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| physical | VI, 201 S. graph. Darst. |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Van Assche, Walter 1958- Verfasser (DE-588)111317088 aut Asymptotics for orthogonal polynomials Walter van Assche Berlin [u.a.] Springer 1987 VI, 201 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1265 Literaturverz. S. [181] - 195 Polynômes orthogonaux - Théorie asymptotique Polynômes orthogonaux - Théorie asymptotique ram polynômes orthogonaux probabilités périodicité théorie asymptotique transformation Stieltjes Orthogonal polynomials Asymptotic theory Orthogonale Polynome (DE-588)4172863-4 gnd rswk-swf Asymptotik (DE-588)4126634-1 gnd rswk-swf Asymptote (DE-588)4143275-7 gnd rswk-swf Orthogonale Polynome (DE-588)4172863-4 s Asymptotik (DE-588)4126634-1 s DE-604 Asymptote (DE-588)4143275-7 s Lecture notes in mathematics 1265 (DE-604)BV000676446 1265 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000422084&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Van Assche, Walter 1958- Asymptotics for orthogonal polynomials Lecture notes in mathematics Polynômes orthogonaux - Théorie asymptotique Polynômes orthogonaux - Théorie asymptotique ram polynômes orthogonaux probabilités périodicité théorie asymptotique transformation Stieltjes Orthogonal polynomials Asymptotic theory Orthogonale Polynome (DE-588)4172863-4 gnd Asymptotik (DE-588)4126634-1 gnd Asymptote (DE-588)4143275-7 gnd |
| subject_GND | (DE-588)4172863-4 (DE-588)4126634-1 (DE-588)4143275-7 |
| title | Asymptotics for orthogonal polynomials |
| title_auth | Asymptotics for orthogonal polynomials |
| title_exact_search | Asymptotics for orthogonal polynomials |
| title_full | Asymptotics for orthogonal polynomials Walter van Assche |
| title_fullStr | Asymptotics for orthogonal polynomials Walter van Assche |
| title_full_unstemmed | Asymptotics for orthogonal polynomials Walter van Assche |
| title_short | Asymptotics for orthogonal polynomials |
| title_sort | asymptotics for orthogonal polynomials |
| topic | Polynômes orthogonaux - Théorie asymptotique Polynômes orthogonaux - Théorie asymptotique ram polynômes orthogonaux probabilités périodicité théorie asymptotique transformation Stieltjes Orthogonal polynomials Asymptotic theory Orthogonale Polynome (DE-588)4172863-4 gnd Asymptotik (DE-588)4126634-1 gnd Asymptote (DE-588)4143275-7 gnd |
| topic_facet | Polynômes orthogonaux - Théorie asymptotique polynômes orthogonaux probabilités périodicité théorie asymptotique transformation Stieltjes Orthogonal polynomials Asymptotic theory Orthogonale Polynome Asymptotik Asymptote |
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