Strong asymptotics for extremal errors and polynomials associated with Erdös-type weights:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Harlow, Essex
Longman Scientific & Techn.
1989
|
| Edition: | 1. publ. |
| Series: | Pitman research notes in mathematics series
202 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 240 S. |
| ISBN: | 0582037794 |
Staff View
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| 100 | 1 | |a Lubinsky, Doron S. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Strong asymptotics for extremal errors and polynomials associated with Erdös-type weights |c D. S. Lubinsky |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Harlow, Essex |b Longman Scientific & Techn. |c 1989 | |
| 300 | |a 240 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pitman research notes in mathematics series |v 202 | |
| 650 | 7 | |a Développements asymptotiques |2 ram | |
| 650 | 7 | |a Polynômes orthogonaux |2 ram | |
| 650 | 7 | |a Problèmes extrémaux (mathématiques) |2 ram | |
| 650 | 7 | |a analyse Fourier |2 inriac | |
| 650 | 7 | |a approximation |2 inriac | |
| 650 | 7 | |a expansion asymptotique |2 inriac | |
| 650 | 7 | |a polynômes orthogonaux |2 inriac | |
| 650 | 7 | |a problème extrémal |2 inriac | |
| 650 | 4 | |a Asymptotic expansions | |
| 650 | 4 | |a Extremal problems (Mathematics) | |
| 650 | 4 | |a Orthogonal polynomials | |
| 650 | 0 | 7 | |a Orthogonale Polynome |0 (DE-588)4172863-4 |2 gnd |9 rswk-swf |
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| 650 | 0 | 7 | |a Asymptotik |0 (DE-588)4126634-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Asymptotische Entwicklung |0 (DE-588)4112609-9 |2 gnd |9 rswk-swf |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
1. Notation 1
2. Statement of Main Results 5
Definition 2.1: SE and SE(j) 6
Theorem 2.2: Extremal Errors and Extremal Polynomials 8
Theorem 2.3: Christoffel Functions on 1R 10
Theorem 2.4: Orthonormal Polynomials on 1R 12
Theorem 2.5: Largest Zeros of Extremal Polynomials 14
Theorem 2.6: Markov—Bernstein Inequalities 15
3. Preliminaries 16
4. Potentials and Majorisation Functions 27
5. Infinite—Finite Range Inequalities 45
Theorem 5.1: The L Case 45
00
Theorem 5.2: The L Case 46
6. Entire Functions 52
Theorem 6.1: Asymptotic Behaviour of Gq 52
7. Largest Zeros of Extremal Polynomials 70
Theorem 7.1: Largest Zeros and Proof of Theorem 2.5 70
Corollary 7.2: Points of Equioscillation 70
Corollary 7.3: Markov—Bernstein Inequalities; Theorem 2.6 71
8. Approximation with Weighted Polynomials 79
Theorem 8.1: Approximation by Pn(x)/H(anx) 79
9. One Sided Weighted Polynomial Approximation 89
Theorem 9.1: One ^ided Approximation by P (x)/H(c x) 89
10. One—Sided Weighted Polynomial Approximation, II 103
Theorem 10.1: One—sided Approximation by P (x)W(c x) 103
Lemma 10.2: Relative Approximation of 1/(Gq /«W) 104
11. Explicit Extremal Polynomials, Christoffel Functions and Szego Functions 111
12. Extremal Errors and Extremal Polynomials 130
Theorem 12.1: Extremal Errors; Theorem 2.2(a) 130
Theorem 12.2: Extremal Polynomials; Theorem 2.2(b) 132
13. Asymptotics of Orthogonal Polynomials on K 136
Theorem 13.1: 1/Gq/2 and [ jt.jt] 136
Theorem 13.2: W2 and [—7r,tt] 138
Theorem 13.4: W2 and R; Theorem 2.4 143
Theorem 13.7: 1/Gq 2 and R 149
14. Mean Asymptotics of Extremal Polynomials 150
Theorem 14.3: Mean Asymptotics; Theorem 2.2(c) 153
Theorem 14.5: Extremal Polynomials; Theorem 2.2(b) 158
15. Christoffel Functions 160
Theorem 15.1: H~2 and c 160
Theorem 15.3: H~2 and an 166
Theorem 15.5: W2 175
References 179
Appendix: Freud Weights 182
I. Main Results 183
Definition I.I: FRA and FRA(j) 183
Theorem 1.2: Christoffel Functions 183
Theorem 1.3: Christoffel Functions 185
Theorem 1.4: Orthogonal Polynomials 187
II. Preliminaries 189
III. Approximation with Weighted Polynomials 194
Theorem III.l: Approximation by P (x)/H(a x) 194
IV. One—Sided Weighted Polynomial Approximation 200
Theorem IV. 1: One sided Approximation by Pn(x)/H(cnx) 200
V. Asymptotics of Orthogonal Polynomials on K 209
Theorem V.I: H~2 and [—x,7r] 209
Lemma V.2: Relative Approximation of 1/(Gq ,^N) 212
Theorem V.3: W and [ x,w] 214
Theorem V.5: W and IR 215
Theorem V.7: H 1 and IR 219
VI. Christoffel Functions 220
Theorem VI. 1: H~2 and cn 220
Theorem VI.3: H~2 and an 226
Theorem VI.5: W2 234
Index 238
|
| any_adam_object | 1 |
| author | Lubinsky, Doron S. |
| author_facet | Lubinsky, Doron S. |
| author_role | aut |
| author_sort | Lubinsky, Doron S. |
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| building | Verbundindex |
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| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
| edition | 1. publ. |
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| id | DE-604.BV001854427 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:36:38Z |
| institution | BVB |
| isbn | 0582037794 |
| language | English |
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| physical | 240 S. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Longman Scientific & Techn. |
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| series | Pitman research notes in mathematics series |
| series2 | Pitman research notes in mathematics series |
| spelling | Lubinsky, Doron S. Verfasser aut Strong asymptotics for extremal errors and polynomials associated with Erdös-type weights D. S. Lubinsky 1. publ. Harlow, Essex Longman Scientific & Techn. 1989 240 S. txt rdacontent n rdamedia nc rdacarrier Pitman research notes in mathematics series 202 Développements asymptotiques ram Polynômes orthogonaux ram Problèmes extrémaux (mathématiques) ram analyse Fourier inriac approximation inriac expansion asymptotique inriac polynômes orthogonaux inriac problème extrémal inriac Asymptotic expansions Extremal problems (Mathematics) Orthogonal polynomials Orthogonale Polynome (DE-588)4172863-4 gnd rswk-swf Extremalpolynom (DE-588)4153425-6 gnd rswk-swf Asymptotik (DE-588)4126634-1 gnd rswk-swf Asymptotische Entwicklung (DE-588)4112609-9 gnd rswk-swf Extremalproblem (DE-588)4439315-5 gnd rswk-swf Extremalproblem (DE-588)4439315-5 s DE-604 Asymptotische Entwicklung (DE-588)4112609-9 s Orthogonale Polynome (DE-588)4172863-4 s Extremalpolynom (DE-588)4153425-6 s Asymptotik (DE-588)4126634-1 s Pitman research notes in mathematics series 202 (DE-604)BV000022845 202 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001227965&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lubinsky, Doron S. Strong asymptotics for extremal errors and polynomials associated with Erdös-type weights Pitman research notes in mathematics series Développements asymptotiques ram Polynômes orthogonaux ram Problèmes extrémaux (mathématiques) ram analyse Fourier inriac approximation inriac expansion asymptotique inriac polynômes orthogonaux inriac problème extrémal inriac Asymptotic expansions Extremal problems (Mathematics) Orthogonal polynomials Orthogonale Polynome (DE-588)4172863-4 gnd Extremalpolynom (DE-588)4153425-6 gnd Asymptotik (DE-588)4126634-1 gnd Asymptotische Entwicklung (DE-588)4112609-9 gnd Extremalproblem (DE-588)4439315-5 gnd |
| subject_GND | (DE-588)4172863-4 (DE-588)4153425-6 (DE-588)4126634-1 (DE-588)4112609-9 (DE-588)4439315-5 |
| title | Strong asymptotics for extremal errors and polynomials associated with Erdös-type weights |
| title_auth | Strong asymptotics for extremal errors and polynomials associated with Erdös-type weights |
| title_exact_search | Strong asymptotics for extremal errors and polynomials associated with Erdös-type weights |
| title_full | Strong asymptotics for extremal errors and polynomials associated with Erdös-type weights D. S. Lubinsky |
| title_fullStr | Strong asymptotics for extremal errors and polynomials associated with Erdös-type weights D. S. Lubinsky |
| title_full_unstemmed | Strong asymptotics for extremal errors and polynomials associated with Erdös-type weights D. S. Lubinsky |
| title_short | Strong asymptotics for extremal errors and polynomials associated with Erdös-type weights |
| title_sort | strong asymptotics for extremal errors and polynomials associated with erdos type weights |
| topic | Développements asymptotiques ram Polynômes orthogonaux ram Problèmes extrémaux (mathématiques) ram analyse Fourier inriac approximation inriac expansion asymptotique inriac polynômes orthogonaux inriac problème extrémal inriac Asymptotic expansions Extremal problems (Mathematics) Orthogonal polynomials Orthogonale Polynome (DE-588)4172863-4 gnd Extremalpolynom (DE-588)4153425-6 gnd Asymptotik (DE-588)4126634-1 gnd Asymptotische Entwicklung (DE-588)4112609-9 gnd Extremalproblem (DE-588)4439315-5 gnd |
| topic_facet | Développements asymptotiques Polynômes orthogonaux Problèmes extrémaux (mathématiques) analyse Fourier approximation expansion asymptotique polynômes orthogonaux problème extrémal Asymptotic expansions Extremal problems (Mathematics) Orthogonal polynomials Orthogonale Polynome Extremalpolynom Asymptotik Asymptotische Entwicklung Extremalproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001227965&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000022845 |
| work_keys_str_mv | AT lubinskydorons strongasymptoticsforextremalerrorsandpolynomialsassociatedwitherdostypeweights |