The functional method and its applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Providence, RI
American Math. Soc.
1970
|
| Series: | Translations of mathematical monographs
28. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Russ. übers. - EST: Metod funkcionalov i ego priloženija (engl.) |
| Physical Description: | VI, 203 S. |
| ISBN: | 0821815784 |
Staff View
MARC
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| 245 | 1 | 0 | |a The functional method and its applications |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 1970 | |
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Record in the Search Index
| _version_ | 1804117250994601984 |
|---|---|
| adam_text | Table of Contents
Introduction 1
1. Moment sequences and Hausdorff s theorems 1
2. The linear functional determined by a moment sequence 9
Part One. Extremal Polynomials of Finite Functionals
Chapter I. Segment functionals on Polynomials 14
1. Extremal polynomials of a moment sequence 14
2. Absolutely monotonic segments and their best extension 21
3. The non absolutely monotonic segment and its extremal
polynomials 33
4. Cebysev polynomials in the critical intervals 39
Chapter II. Properties of the Norm; Segments of the First and
Second Classes 49
1. The norm as a function of the elements 49
2. Segments of class I 53
3. Faithful and fictitious distributions of a segment 57
4. Some sufficient conditions for a segment to belong to class II . . 60
5. Variable segment functionals 64
Chapter III. Families of Extremal Polynomials 69
1. Construction of segments with given distribution 69
2. Parametrization of families of polynomials 72
3. Determined segment functionals 77
Chapter IV. Polynomials of Passport [n,n,0] 81
1. Determining segments for [re, re, 0] polynomials 81
2. Analytic construction of [re, re, 0] polynomials 91
3. Some metric properties of [re, re, 0] polynomials 99
Chapter V. Polynomials of Passport [re, re, 1] 103
1. Existence and nature of deformation of [re, re, l] polynomials . . . 103
2. Methods of constructing [re, re, l] polynomials in the simplest
cases 107
3. General analytic construction of [re, n,l] polynomials 112
V
vi CONTENTS
Chapter VI. Polynomials of Passport [n, n — 1,0] 117
1. Determining functional and qualitative investigation 117
2. Equations of the boundary of the region M 123
3. Analytic construction of [n, n — 1,0] polynomials 126
Part Two. PROBLEMS OF CEBYSEV APPROXIMATION
Chapter I. Polynomials of Least Deviation for Some Classical
Problems 133
1. V. A. Markov s problem 133
2. The Zolotarev Pseborskii problem 137
3. N. I. Ahiezer s problem and its solution by the functional
method 143
Chapter II. Best Uniform Approximation of Polynomials and Analytic
Functions 146
1. Approximation of polynomials 146
2. Approximation of analytic functions 149
Chapter III. The First Derivative Functional and A. A. Markov s
Problem 156
1. Extremal polynomials of the derivative functional 156
2. The norm of the derivative functional on [0,1] 162
Chapter IV. The Trigonometric Functionals Fpcoe and Fpsin and In¬
equalities for Polynomials in the Complex Plane 168
1. Stability of trigonometric functionals 168
2. Asymptotic behavior of the Zolotarev regions in the z plane . . . 171
Bibliography 177
Appendix: V. A. Gusev, Derivative Functionals of an Algebraic
Polynomial and V. A. Markov s Theorem 179
Index of Numbered Examples 199
Index of Numbered Theorems 199
Subject Index 201
|
| any_adam_object | 1 |
| author | Voronovskaja, E. V. |
| author_facet | Voronovskaja, E. V. |
| author_role | aut |
| author_sort | Voronovskaja, E. V. |
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| dewey-full | 517/.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 517 - [Unassigned] |
| dewey-raw | 517/.5 |
| dewey-search | 517/.5 |
| dewey-sort | 3517 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre | Endliche Funktional gnd |
| genre_facet | Endliche Funktional |
| id | DE-604.BV002959543 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:51:26Z |
| institution | BVB |
| isbn | 0821815784 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001852833 |
| oclc_num | 108128 |
| open_access_boolean | |
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| physical | VI, 203 S. |
| psigel | TUB-nvmb |
| publishDate | 1970 |
| publishDateSearch | 1970 |
| publishDateSort | 1970 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Voronovskaja, E. V. Verfasser aut Metod funkcionalov i ego priloženija The functional method and its applications Providence, RI American Math. Soc. 1970 VI, 203 S. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 28. Aus d. Russ. übers. - EST: Metod funkcionalov i ego priloženija (engl.) Chebyshev, Polynomes Fonctions (Mathématiques) Chebyshev approximation Functions Extremalpolynom (DE-588)4153425-6 gnd rswk-swf Čebyšev-Approximation (DE-588)4147433-8 gnd rswk-swf Approximationstheorie (DE-588)4120913-8 gnd rswk-swf Endliche Funktional gnd rswk-swf Čebyšev-Approximation (DE-588)4147433-8 s DE-604 Extremalpolynom (DE-588)4153425-6 s Endliche Funktional f Approximationstheorie (DE-588)4120913-8 s Translations of mathematical monographs 28. (DE-604)BV000002394 28. HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001852833&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Voronovskaja, E. V. The functional method and its applications Translations of mathematical monographs Chebyshev, Polynomes Fonctions (Mathématiques) Chebyshev approximation Functions Extremalpolynom (DE-588)4153425-6 gnd Čebyšev-Approximation (DE-588)4147433-8 gnd Approximationstheorie (DE-588)4120913-8 gnd |
| subject_GND | (DE-588)4153425-6 (DE-588)4147433-8 (DE-588)4120913-8 |
| title | The functional method and its applications |
| title_alt | Metod funkcionalov i ego priloženija |
| title_auth | The functional method and its applications |
| title_exact_search | The functional method and its applications |
| title_full | The functional method and its applications |
| title_fullStr | The functional method and its applications |
| title_full_unstemmed | The functional method and its applications |
| title_short | The functional method and its applications |
| title_sort | the functional method and its applications |
| topic | Chebyshev, Polynomes Fonctions (Mathématiques) Chebyshev approximation Functions Extremalpolynom (DE-588)4153425-6 gnd Čebyšev-Approximation (DE-588)4147433-8 gnd Approximationstheorie (DE-588)4120913-8 gnd |
| topic_facet | Chebyshev, Polynomes Fonctions (Mathématiques) Chebyshev approximation Functions Extremalpolynom Čebyšev-Approximation Approximationstheorie Endliche Funktional |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001852833&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
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