Introduction to the theory of weighted polynomial approximation:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
1996
|
| Series: | Series in approximations and decompositions
7 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 379 S. |
| ISBN: | 9810213123 |
Staff View
MARC
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| 245 | 1 | 0 | |a Introduction to the theory of weighted polynomial approximation |c H. N. Mhaskar |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 1996 | |
| 300 | |a XIV, 379 S. | ||
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| 490 | 1 | |a Series in approximations and decompositions |v 7 | |
| 650 | 4 | |a Ortogonal polinomlar | |
| 650 | 4 | |a Yaklaştırma teorisi | |
| 650 | 4 | |a Approximation theory | |
| 650 | 4 | |a Orthogonal polynomials | |
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Record in the Search Index
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| adam_text | Contents
Preface ix
1. Orthogonal Polynomials 1
1.1. Elementary facts 1
1.2. Interpolation and quadrature 10
1.3. Extremal properties 18
1.4. Some estimates 23
2. Approximation on [ 1,1] 27
2.1. Inequalities for trigonometric polynomials 27
2.2. Favard type estimates 33
2.3. A K functional and the degree of approximation 40
3. Freud Polynomials 46
3.1. The weight function and orthogonal polynomials 46
3.2. Christoffel functions 55
3.3. An alternative approach 65
3.4. Polynomial inequalities 70
4. Degree of Approximation 80
4.1. Favard type estimates 80
4.2. Direct and converse theorems 91
4.3. The Fourier transform 101
5. The ^ functional , 106
5.1. A smooth weight function 106
5.2. A modulus of smoothness 112
5.3. Alternative expressions 119
xiii
xiv Contents
6. Potential Theory 124
6.1. Where does the sup norm live? 124
6.2. Where does the LP norm live? 139
6.3. Some extremal polynomials 152
6.4. The prototypical Freud weights 166
7. Approximation of Entire Functions 171
7.1. Classical results 171
7.2. Functions with finite order and type 177
7.3. Functions of finite exponential type 186
8. Freud Polynomials II 191
8.1. The interior bounds 191
8.2. The Lubinsky entire function 200
8.3. The largest zero 214
9. Processes of Approximation 221
9.1. Functions of bounded variation 222
9.2. Interpolation and quadrature 234
9.3. Strip of convergence 245
10. A Density Theorem 253
10.1. The contour integral approach 253
10.2. Discretization of the potential 265
10.3. The strong asymptotics 276
11. Applications 290
11.1. Weighted potentials 290
11.2. Gaussian networks 305
11.3. Wavelets 314
Appendix 320
Notes 333
References 339
Subject Index 347
Bibliography 355
|
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| id | DE-604.BV011323876 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:07:49Z |
| institution | BVB |
| isbn | 9810213123 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007608593 |
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| physical | XIV, 379 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | World Scientific |
| record_format | marc |
| series | Series in approximations and decompositions |
| series2 | Series in approximations and decompositions |
| spelling | Mhaskar, Hrushikesh N. 1956- Verfasser (DE-588)10437019X aut Introduction to the theory of weighted polynomial approximation H. N. Mhaskar Singapore [u.a.] World Scientific 1996 XIV, 379 S. txt rdacontent n rdamedia nc rdacarrier Series in approximations and decompositions 7 Ortogonal polinomlar Yaklaştırma teorisi Approximation theory Orthogonal polynomials Approximationstheorie (DE-588)4120913-8 gnd rswk-swf Orthogonale Polynome (DE-588)4172863-4 gnd rswk-swf Approximationstheorie (DE-588)4120913-8 s Orthogonale Polynome (DE-588)4172863-4 s DE-604 Series in approximations and decompositions 7 (DE-604)BV009569075 7 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007608593&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mhaskar, Hrushikesh N. 1956- Introduction to the theory of weighted polynomial approximation Series in approximations and decompositions Ortogonal polinomlar Yaklaştırma teorisi Approximation theory Orthogonal polynomials Approximationstheorie (DE-588)4120913-8 gnd Orthogonale Polynome (DE-588)4172863-4 gnd |
| subject_GND | (DE-588)4120913-8 (DE-588)4172863-4 |
| title | Introduction to the theory of weighted polynomial approximation |
| title_auth | Introduction to the theory of weighted polynomial approximation |
| title_exact_search | Introduction to the theory of weighted polynomial approximation |
| title_full | Introduction to the theory of weighted polynomial approximation H. N. Mhaskar |
| title_fullStr | Introduction to the theory of weighted polynomial approximation H. N. Mhaskar |
| title_full_unstemmed | Introduction to the theory of weighted polynomial approximation H. N. Mhaskar |
| title_short | Introduction to the theory of weighted polynomial approximation |
| title_sort | introduction to the theory of weighted polynomial approximation |
| topic | Ortogonal polinomlar Yaklaştırma teorisi Approximation theory Orthogonal polynomials Approximationstheorie (DE-588)4120913-8 gnd Orthogonale Polynome (DE-588)4172863-4 gnd |
| topic_facet | Ortogonal polinomlar Yaklaştırma teorisi Approximation theory Orthogonal polynomials Approximationstheorie Orthogonale Polynome |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007608593&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT mhaskarhrushikeshn introductiontothetheoryofweightedpolynomialapproximation |