Christoffel functions and orthogonal polynomials for exponential weights on [-1,1]
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| Hauptverfasser: | , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
1994
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| Schriftenreihe: | American Mathematical Society: Memoirs of the American Mathematical Society
535 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 245 | 1 | 0 | |a Christoffel functions and orthogonal polynomials for exponential weights on [-1,1] |c A. L. Levin ; D. S. Lubinsky |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 1994 | |
| 300 | |a XIII, 146 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a American Mathematical Society: Memoirs of the American Mathematical Society |v 535 | |
| 500 | |a Volume 111, Number 535 (fourth of 5 numbers) | ||
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| 650 | 0 | 7 | |a Christoffel-Darboux-Formel |0 (DE-588)4365527-0 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Lubinsky, Doron S. |d 1955- |e Verfasser |0 (DE-588)172232589 |4 aut | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102/MAT 001z 2001 B 990-532/536 |
|---|---|
| DE-BY-TUM_katkey | 1441318 |
| DE-BY-TUM_local_keycode | ug |
| DE-BY-TUM_media_number | 040010666832 |
| _version_ | 1816712326282215424 |
| adam_text | TABLE OF CONTENTS
§1. Introduction and Results 1
Definition 1.1: The class W 5
Theorem 1.2: Christoffel Functions 7
Corollary 1.3: Sup Norms of Christoffel Functions 8
Corollary 1.4: Zeros 9
Corollary 1.5: Bounds on Orthonormal Polynomials 10
Theorem 1.6: Sup Norm Christoffel Functions 12
Theorem 1.7: Restricted Range Inequalities 12
Theorem 1.8: L Norms of Orthonormal Polynomials 12
§2. Some Ideas Behind the Proofs 14
I. An Orthogonal Polynomial Angle 14
II. The Potential Theory Side: Lower Bounds for An 16
III. The Potential Theory Side: Upper Bounds for An 18
IV. The Orthogonal Polynomials Angle: An(x) 19
§3. Technical Estimates 22
Lemma 3.1: Estimates involving Q 22
Lemma 3.2: Estimates involving au 24
Lemma 3.3: More estimates involving au 29
Lemma 3.4: Estimates for An(s, t) 32
Lemma 3.5: Differences involving An(s,t) 33
§4. Estimates for the Density Functions /zn 36
Lemma 4.1: Old estimates for nn 36
v
vi CONTENTS
Theorem 4.2: Estimates for fin on all of ( 1,1) 37
Theorem 4.3: Differences involving nn 37
Proof of Theorem 4.2 40
Proof of Theorem 4.3 (b) 42
Proof of Theorem 4.3 (a) 44
§5. Majorization Functions and Integral Equations 49
Lemma 5.1: Old Potential Theory/Integral Equations 49
Lemma 5.2: Estimates for Bn R,vnR 51
Theorem 5.3: Estimates for UnR 53
§6. The Proof of Theorem 1.7 57
Lemma 6.1: Lp Bounds for Weighted Polynomials 57
Proof of Theorem 1.7 58
§7. Lower Bounds for Xn 63
Theorem 7.1: Lower Bounds for An 63
Lemma 7.2: Preliminary Lower Bounds 64
Proof of Theorem 7.1 66
§8. Discretisation of a Potential: Theorem 1.6 71
Theorem 8.1: One Point Polynomials 71
Deduction of Theorem 1.6 71
Theorem 8.2: The Bounds for Tn 73
Deduction of Theorem 8.1 73
Lemma 8.3: Estimates for the discretisation points 75
Lemma 8.4: Estimates for St + S4 77
Lemma 8.5: Estimates for Ay 79
Lemma 8.6: Estimates for r • 82
Lemma 8.7: Estimates for S2l 85
CONTENTS vii
Lemma 8.8: Lower Bounds for 52 88
Lemma 8.9: Upper Bounds for 52 89
Lemma 8.10: Bounds for 5S 93
Proof of Theorem 8.2 96
§9. Upper Bounds for An: Theorems 1.2 and Corollary 1.3 97
Lemma 9.1: Preliminary Upper Bounds for An 97
Proof of Theorem 1.2 99
Proof of Corollary 1.3 102
§10. Zeros: Corollary 1.4 103
Proof of Corollary 1.4 (i) 103
Lemma 10.1: Series Equivalent to w~2 106
Proof of a Weaker Form of Corollary 1.4 (ii) 109
§11. Bounds on Orthogonal Polynomials: Corollary 1.5 112
Lemma 11.1: An Identity for p n(xjn) 113
Lemma 11.2: A Bound for Ix 114
Lemma 11.3: An Integral Estimate 119
Lemma 11.4: An Estimate for I2 120
Lemma 11.5: An Estimate for 73 121
Theorem 11.6: Implicit Bounds for An 124
Proof of the Upper Bounds for Orthogonal Polynomials 125
Lemma 11.7: A Further Integral Estimate 127
Theorem 11.8: Good Estimates for An 129
Proof of Corollary 1.5 (iii) 130
Lemma 11.9: A Markov Bernstein Inequality 131
Proof of the Lower Bounds for Orthogonal Polynomials 131
§12. Lp Norms of Orthonormal Polynomials: Theorem 1.8 133
viii CONTENTS
Upper Bounds for Lp Norms of Orthonormal Polynomials 133
Lemma 12.2: Fundamental Polynomials of Interpolation 134
Lower Bounds for L Norms of Orthonormal Polynomials 140
Proof of Corollary 1.4 (ii) 141
References 142
|
| any_adam_object | 1 |
| author | Lēwîn, Ēlî 1944- Lubinsky, Doron S. 1955- |
| author_GND | (DE-588)123172373 (DE-588)172232589 |
| author_facet | Lēwîn, Ēlî 1944- Lubinsky, Doron S. 1955- |
| author_role | aut aut |
| author_sort | Lēwîn, Ēlî 1944- |
| author_variant | ē l ēl d s l ds dsl |
| building | Verbundindex |
| bvnumber | BV009896252 |
| classification_rvk | SI 130 |
| classification_tum | MAT 266f |
| ctrlnum | (OCoLC)472295158 (DE-599)BVBBV009896252 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV009896252 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-25T17:19:56Z |
| institution | BVB |
| isbn | 0821825992 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006553383 |
| oclc_num | 472295158 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-384 DE-12 DE-739 DE-29T DE-824 DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-83 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-384 DE-12 DE-739 DE-29T DE-824 DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-83 DE-188 |
| physical | XIII, 146 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | American Mathematical Society: Memoirs of the American Mathematical Society |
| series2 | American Mathematical Society: Memoirs of the American Mathematical Society |
| spellingShingle | Lēwîn, Ēlî 1944- Lubinsky, Doron S. 1955- Christoffel functions and orthogonal polynomials for exponential weights on [-1,1] American Mathematical Society: Memoirs of the American Mathematical Society Konvergenz (DE-588)4032326-2 gnd Christoffel-Darboux-Formel (DE-588)4365527-0 gnd Orthogonale Polynome (DE-588)4172863-4 gnd |
| subject_GND | (DE-588)4032326-2 (DE-588)4365527-0 (DE-588)4172863-4 |
| title | Christoffel functions and orthogonal polynomials for exponential weights on [-1,1] |
| title_auth | Christoffel functions and orthogonal polynomials for exponential weights on [-1,1] |
| title_exact_search | Christoffel functions and orthogonal polynomials for exponential weights on [-1,1] |
| title_full | Christoffel functions and orthogonal polynomials for exponential weights on [-1,1] A. L. Levin ; D. S. Lubinsky |
| title_fullStr | Christoffel functions and orthogonal polynomials for exponential weights on [-1,1] A. L. Levin ; D. S. Lubinsky |
| title_full_unstemmed | Christoffel functions and orthogonal polynomials for exponential weights on [-1,1] A. L. Levin ; D. S. Lubinsky |
| title_short | Christoffel functions and orthogonal polynomials for exponential weights on [-1,1] |
| title_sort | christoffel functions and orthogonal polynomials for exponential weights on 1 1 |
| topic | Konvergenz (DE-588)4032326-2 gnd Christoffel-Darboux-Formel (DE-588)4365527-0 gnd Orthogonale Polynome (DE-588)4172863-4 gnd |
| topic_facet | Konvergenz Christoffel-Darboux-Formel Orthogonale Polynome |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006553383&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT lewineli christoffelfunctionsandorthogonalpolynomialsforexponentialweightson11 AT lubinskydorons christoffelfunctionsandorthogonalpolynomialsforexponentialweightson11 |