Series of Faber polynomials:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam [u.a.]
Gordon and Breach Science Publ.
1998
|
| Series: | Analytical methods and special functions
1 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | XX, 301 S. |
| ISBN: | 9056990586 |
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MARC
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| 100 | 1 | |a Suetin, Pavel K. |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Riad mnogochlenov Faber |
| 245 | 1 | 0 | |a Series of Faber polynomials |c P. K. Suetin |
| 264 | 1 | |a Amsterdam [u.a.] |b Gordon and Breach Science Publ. |c 1998 | |
| 300 | |a XX, 301 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Analytical methods and special functions |v 1 | |
| 500 | |a Aus dem Russ. übers. | ||
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Record in the Search Index
| _version_ | 1804126520239718400 |
|---|---|
| adam_text | CONTENTS
Preface ix
Preface to the English Edition xv
Notation xix
Chapter I. Some results of approximation theory 1
§ 1. The best approximations of real functions 1
§ 2. Lebesgue inequalities for Fourier and Taylor series 7
§ 3. Jackson approximating sums 15
§ 4. Estimates of the Fourier and Taylor coefficients 22
§ 5. Analogues of the Weierstrass theorem on approximation
in a complex domain 28
Chapter II. The elementary properties of Faber polynomials 33
§ 1. Fundamental definitions and examples 33
§ 2. Algebraic properties of Faber polynomials 39
§ 3. The simplest asymptotic properties 42
§ 4. Generalized Faber polynomials 44
Chapter III. Faber series with the simplest conditions 49
§ 1. Faber polynomial series 49
§ 2. Faber series of analytic functions 51
§ 3. The direct theorem of Bernstein Walsh 54
§ 4. The inverse theorem of Bernstein Walsh 56
Chapter IV. Asymptotic properties of Faber polynomials 60
§ 1. Estimation of Faber polynomials inside a domain 60
§ 2. Asymptotic representations outside a domain 62
§ 3. Faber polynomials with singularities of the weight function 70
§ 4. Faber polynomials with singularities of the contour 73
Chapter V. Convergence of Faber series inside a domain 77
§ 1. Some conditions for convergence inside a domain 77
§ 2. The main theorem of Faber series 83
§ 3. Expansion of Cauchy type integrals with respect to area 86
§ 4. The table of conditions for Faber series convergence 90
§ 5. Generalized Faber series 93
v
vi CONTENTS
Chapter VI. Series of Faber polynomials 100
§ 1. Conditions for convergence inside a domain 100
§ 2. Boundary properties of series of Faber polynomials 103
§ 3. Uniqueness of Faber polynomial series 108
§ 4. Series of generalized Faber polynomials 113
Chapter VII. Some properties of Faber operators 117
§ 1. The Faber operator and its simplest properties 117
§ 2. Boundary properties of Faber operators 120
§ 3. Estimates of the norms of Faber operators 123
§ 4. Transformation of rational and meromorphic functions 128
§ 5. Generalized Faber operators 131
Chapter VIII. Faber series in a closed domain 136
§ 1. Domains with a strongly smooth boundary 136
§ 2. Theorem concerning the inverse Faber operator 142
§ 3. Al per s principal results 148
§ 4. Another summation formula 156
§ 5. Generalized Faber series in a closed domain 160
Chapter IX. Faber polynomials and the theory of univalent
functions 168
§ 1. The method of areas in the theory of univalent functions 168
§ 2. Lebedev s results 172
§ 3. Pommerenke s results for Faber polynomials 177
§ 4. The results of Kovari Pommerenke 184
§ 5. The results of Lesley, Vinge Warschawski 191
Chapter X. Faber series in canonical domains 196
§ 1. The auxiliary properties of Taylor series 196
§ 2. Bounded functions in a canonical domain 199
§ 3. The general case of an arbitrary continuum 205
§ 4. The case of poles on a level line 208
Chapter XI. Faber series and the Riemann boundary problem 214
§ 1. The approximate solution of Riemann problem 214
§ 2. Some properties of Faber series of the second kind 218
§ 3. Faber series and generalized functions 223
§ 4. Riemann problem in the class of generalized functions 230
Chapter XII. The summation formula of Dzyadyk 233
§ 1. Dzyadyk s formula for Faber series summation 233
§ 2. Summation of the generalized Faber series 237
§ 3. Summation of Faber series in a closed domain 241
§ 4. Faber approximation of the Cauchy kernel 245
§ 5. Nikol skii s problem in a complex domain 248
Chapter XIII. Generalization of Faber polynomials and series 252
§ 1. Faber Walsh polynomials 252
§ 2. Faber Laurent series 255
CONTENTS vii
§ 3. Faber Dzhrbashyan rational functions 257
§ 4. Basic systems of Faber Erokhin 262
Chapter XIV. Some recent results 270
§ 1. Faber series of matrices and operators 270
§ 2. Faber operators with singularities of the weight function and
contour 273
§ 3. Faber series with singularities of weight function and contour 276
§ 4. The Faber Dirichlet operator 278
§ 5. The Faber series in the Dirichlet problem 280
Comments and Supplements 283
References 287
Authors Index 297
Subject Index 299
|
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| dewey-tens | 510 - Mathematics |
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| id | DE-604.BV011932993 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:18:45Z |
| institution | BVB |
| isbn | 9056990586 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008066114 |
| oclc_num | 40054965 |
| open_access_boolean | |
| owner | DE-824 DE-83 |
| owner_facet | DE-824 DE-83 |
| physical | XX, 301 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Gordon and Breach Science Publ. |
| record_format | marc |
| series | Analytical methods and special functions |
| series2 | Analytical methods and special functions |
| spelling | Suetin, Pavel K. Verfasser aut Riad mnogochlenov Faber Series of Faber polynomials P. K. Suetin Amsterdam [u.a.] Gordon and Breach Science Publ. 1998 XX, 301 S. txt rdacontent n rdamedia nc rdacarrier Analytical methods and special functions 1 Aus dem Russ. übers. Polynomials Series Analytical methods and special functions 1 (DE-604)BV011932737 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008066114&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Suetin, Pavel K. Series of Faber polynomials Analytical methods and special functions Polynomials Series |
| title | Series of Faber polynomials |
| title_alt | Riad mnogochlenov Faber |
| title_auth | Series of Faber polynomials |
| title_exact_search | Series of Faber polynomials |
| title_full | Series of Faber polynomials P. K. Suetin |
| title_fullStr | Series of Faber polynomials P. K. Suetin |
| title_full_unstemmed | Series of Faber polynomials P. K. Suetin |
| title_short | Series of Faber polynomials |
| title_sort | series of faber polynomials |
| topic | Polynomials Series |
| topic_facet | Polynomials Series |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008066114&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011932737 |
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