Orthogonal polynomials for exponential weights:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2001
|
| Schriftenreihe: | CMS books in mathematics
4 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 455 - 469 |
| Beschreibung: | XI, 476 S. 24 cm |
| ISBN: | 0387989412 |
Internformat
MARC
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| 100 | 1 | |a Lēwîn, Ēlî |d 1944- |e Verfasser |0 (DE-588)123172373 |4 aut | |
| 245 | 1 | 0 | |a Orthogonal polynomials for exponential weights |c Eli Levin ; Doron S. Lubinsky. [Canadian Mathematical Society] |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2001 | |
| 300 | |a XI, 476 S. |b 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a CMS books in mathematics |v 4 | |
| 500 | |a Literaturverz. S. 455 - 469 | ||
| 650 | 4 | |a Orthogonale Polynome | |
| 650 | 4 | |a Orthogonal polynomials | |
| 650 | 4 | |a Convergence | |
| 650 | 0 | 7 | |a Orthogonale Polynome |0 (DE-588)4172863-4 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Lubinsky, Doron S. |e Verfasser |4 aut | |
| 830 | 0 | |a CMS books in mathematics |v 4 |w (DE-604)BV013248581 |9 4 | |
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Datensatz im Suchindex
| _version_ | 1804128836276715520 |
|---|---|
| adam_text | Contents
1 Introduction and Results 1
1.1 Background 1
1.2 Classes of Weights 6
1.3 Inequalities 14
1.4 Orthogonal Polynomials: Bounds 21
1.5 Asymptotics of Extremal and Orthonormal Polynomials . . 23
1.6 Specific Examples 27
2 Weighted Potential Theory: The Basics 35
2.1 Equilibrium Measures 35
2.2 Rakhmanov s Representation for Q 45
2.3 A Formula for aj 51
2.4 Further Identities Involving at 56
3 Basic Estimates for Q,at 63
3.1 Estimates involving Q 64
3.2 Estimates involving a±t, Part 1 68
3.3 Estimates involving a±t, Part 2 79
3.4 A Weight in T T (Dini) 91
4 Restricted Range Inequalities 95
5 Estimates for Measure and Potential 109
5.1 Statement of Results 109
X
5.2 Lower Bounds 113
5.3 Upper Bounds 114
5.4 Estimates for ipt 125
5.5 Estimation of Potential 129
6 Smoothness of at 145
6.1 Statement of Results 145
6.2 Outline of the Proof and Technical Lemmas 150
6.3 The Proof of Theorem 6.3 157
6.4 Proof of Theorem 6.2 165
7 Weighted Polynomial Approximation 169
7.1 Statement of Results 169
7.2 Setting up the Discretisation 174
7.3 The Proof of Theorems 7.1 7.4 176
7.4 One Sided Approximation 183
7.5 Properties of the Discretisation Points 186
7.6 The Tail Terms 195
7.7 The Central Terms 201
7.8 Global Bounds 206
7.9 Derivatives of Discretised Polynomials 212
7.10 Proof of Theorem 7.5 227
8 Asymptotics of Extremal Errors 231
8.1 Statement of Results 231
8.2 Proof of Theorem 8.1 234
8.3 Proof of Theorem 8.2 239
8.4 Proof of Theorem 8.3 248
9 Christoffel Functions 253
9.1 Statement of Results 253
9.2 Proof of Theorem 9.1 258
9.3 Lower Bounds for Lp Christoffel Functions 260
9.4 Upper Bounds for Christoffel Functions 265
9.5 Christoffel Functions for Bernstein Szego Weights 271
9.6 Asymptotic Lower Bounds for Christoffel Functions 273
9.7 Asymptotic Upper Bounds for Christoffel Functions .... 280
10 Markov Bernstein and Nikolskii Inequalities 293
10.1 Statement of Results 293
10.2 Bernstein Inequalities for p = oo 295
10.3 Bernstein Inequalities for p oo 298
10.4 Proof of the Nikolskii Inequalities 308
11 Zeros of Orthogonal Polynomials 313
11.1 Statement of Results 313
xi
11.2 The Largest Zeros 315
11.3 Spacing of Zeros 320
12 Bounds on Orthogonal Polynomials 325
12.1 The Essence of the Proof 326
12.2 Some Technicalities Involving Q 333
12.3 Integrals Near and Far from x 336
12.4 Non negative x 341
12.5 Negative x 350
13 Further Bounds and Applications 359
13.1 Statement of Results 359
13.2 Estimation of A^(x) 362
13.3 The Proof of Theorem 13.2 369
13.4 Lagrange Interpolation Polynomials 371
13.5 Proof of the Corollaries 380
14 Asymptotics of Extremal Polynomials 385
14.1 Statement of Results 385
14.2 Technical Lemmas 388
14.3 Proof of Theorem 14.1 391
14.4 Proof of Theorem 14.2 394
15 Asymptotics of Orthonormal Polynomials 401
15.1 Statement of Results 401
15.2 Proof of Theorem 15.2 404
15.3 Proof of Theorem 15.3 409
A Bernstein Szego Lp Extremal Polynomials 419
B Bernstein Szego Orthogonal Polynomials 435
Notes 447
References 455
List of Symbols 471
Index 475
|
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| author | Lēwîn, Ēlî 1944- Lubinsky, Doron S. |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 230 SK 470 |
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| dewey-full | 515/.5521 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.55 21 |
| dewey-search | 515/.55 21 |
| dewey-sort | 3515 255 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV013982581 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:55:34Z |
| institution | BVB |
| isbn | 0387989412 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009571981 |
| oclc_num | 248097540 |
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| physical | XI, 476 S. 24 cm |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| series | CMS books in mathematics |
| series2 | CMS books in mathematics |
| spelling | Lēwîn, Ēlî 1944- Verfasser (DE-588)123172373 aut Orthogonal polynomials for exponential weights Eli Levin ; Doron S. Lubinsky. [Canadian Mathematical Society] New York [u.a.] Springer 2001 XI, 476 S. 24 cm txt rdacontent n rdamedia nc rdacarrier CMS books in mathematics 4 Literaturverz. S. 455 - 469 Orthogonale Polynome Orthogonal polynomials Convergence Orthogonale Polynome (DE-588)4172863-4 gnd rswk-swf Orthogonale Polynome (DE-588)4172863-4 s DE-604 Lubinsky, Doron S. Verfasser aut CMS books in mathematics 4 (DE-604)BV013248581 4 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009571981&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lēwîn, Ēlî 1944- Lubinsky, Doron S. Orthogonal polynomials for exponential weights CMS books in mathematics Orthogonale Polynome Orthogonal polynomials Convergence Orthogonale Polynome (DE-588)4172863-4 gnd |
| subject_GND | (DE-588)4172863-4 |
| title | Orthogonal polynomials for exponential weights |
| title_auth | Orthogonal polynomials for exponential weights |
| title_exact_search | Orthogonal polynomials for exponential weights |
| title_full | Orthogonal polynomials for exponential weights Eli Levin ; Doron S. Lubinsky. [Canadian Mathematical Society] |
| title_fullStr | Orthogonal polynomials for exponential weights Eli Levin ; Doron S. Lubinsky. [Canadian Mathematical Society] |
| title_full_unstemmed | Orthogonal polynomials for exponential weights Eli Levin ; Doron S. Lubinsky. [Canadian Mathematical Society] |
| title_short | Orthogonal polynomials for exponential weights |
| title_sort | orthogonal polynomials for exponential weights |
| topic | Orthogonale Polynome Orthogonal polynomials Convergence Orthogonale Polynome (DE-588)4172863-4 gnd |
| topic_facet | Orthogonale Polynome Orthogonal polynomials Convergence |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009571981&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013248581 |
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