Elements of the theory of functions:
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch Russisch |
| Veröffentlicht: |
Oxford [u.a.]
Pergamon Press
1966
|
| Ausgabe: | 1. Engl. ed. |
| Schriftenreihe: | International series of monographs in pure and applied mathematics
90 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002331378&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XII, 219 S. graph. Darst. |
Internformat
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| 240 | 1 | 0 | |a Elementiy teorii funktsii |
| 245 | 1 | 0 | |a Elements of the theory of functions |c R. S. Guter, L. D. Kudryavtsev, B. M. Levitan |
| 250 | |a 1. Engl. ed. | ||
| 264 | 1 | |a Oxford [u.a.] |b Pergamon Press |c 1966 | |
| 300 | |a XII, 219 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a International series of monographs in pure and applied mathematics |v 90 | |
| 650 | 4 | |a Fonctions (Mathématiques) | |
| 650 | 4 | |a Functions | |
| 650 | 0 | 7 | |a Funktionentheorie |0 (DE-588)4018935-1 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Kudrjavcev, Lev Dmitrievič |d 1923-1984 |e Verfasser |0 (DE-588)1070882755 |4 aut | |
| 700 | 1 | |a Levitan, Boris M. |d 1914-2004 |e Verfasser |0 (DE-588)1102396559 |4 aut | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0024 58 A 287-90 |
|---|---|
| DE-BY-TUM_katkey | 1311340 |
| DE-BY-TUM_location | Mag |
| DE-BY-TUM_media_number | TEMP2675091 |
| _version_ | 1821932622286159872 |
| adam_text | CONTENTS
Foreword ix
Editor s Preface to the Russian Edition xi
Chapter I. Functions of a Real Variable
(basic ideas and theorems) 1
§ 1. Linear Point Sets. Power and Category 1
§ 2. The Lebesgue Measure of Linear Sets 16
§ 3. Basic Classes of Functions 22
§ 4. The Derivative and its Generalization 31
§ 5. The Integration of Functions 36
§ 6. Sequences of Functions 52
§ 7. Orthogonal Systems of Functions 60
§ 8. Functions of Several Variables 70
§ 9. Basic Function Spaces 78
Chapter II. The Interpolation and Approximation
of Functions 86
§ 1. Introductory Remarks 86
§ 2. The Interpolation of Functions by Polynomials 87
2.1. The Simplest Interpolation Problem. The Lagrange and
Newtonian Interpolation Polynomials 87
2.2. Interpolation by Trigonometric Polynomials 92
2.3. General Interpolation Problems. Hermite s formula 95
2.4. The Convergence of Interpolation Polynomials 96
2.5. Operations on Interpolation Polynomials Leading to
Convergent Processes 103
2.6. Generalized Interpolation Polynomials 104
2.7. Remarks 105
§ 3. Uniform Approximations of Functions of one Variable by Poly¬
nomials and their Generalizations 107
3.1. General Remarks on the Approximation of Functions 107
3.2. Weierstrass Theorem 108
3.3. Bernstein Polynomials 109
3.4. The Best Uniform Approximations of Functions by Poly¬
nomials of a Given Degree 110
3.5. Chebyshev s Results for Best Approximations 112
3.6. The Approximate Formation of Best Approximating
Chebyshev Polynomials 114
v
Vi CONTENTS
3.7. The Best Approximations to Continuous and Differentiable
Periodic Functions by Trigonometric Polynomials of a
Given Degree 118
3.8. The Best Approximations of Continuous and Differentiable
Functions by Algebraic Polynomials of a Given Degree 123
3.9. The Best Approximations of Functions by Integral Func¬
tions 129
3.10. Weighted Approximations of Functions on the Whole
Numerical Axis 131
§ 4. Methods of Uniform Approximation of Functions 132
4.1. The Approximation of Periodic Functions by Fourier Sums 132
4.2. Linear Methods of Approximation of Periodic Functions by
Trigonometric Polynomials (the methods of Fejer, LaVallee
Poussin and Bernstein—Rogosinski) 135
4.3. Linear Methods of Approximation of Functions by
Algebraic Polynomials 139
4.4. The Best Linear Methods of Approximation of Functions 143
§ 5. The Approximation of Functions of one Variable in the Mean 146
5.1. General Remarks 146
5.2. Best Approximations in the Mean 148
5.3. Systems of Functions which Best Approximate Some Class
of Functions 151
§ 6. The Approximation of Functions of Many Variables 152
6.1. Basic Ideas 152
6.2. The Theory of Best Approximations of Functions of Many
Variables 156
§ 7. The Theory of Approximations in Banach Spaces 158
7.1. General Ideas. Best Approximations in Hilbert Spaces. The
Method of Least Squares for the Construction of best Ap¬
proximations 158
7.2. The Connection Between the Best Approximations and the
Entropy of the Sets 160
7.3. The Theory of Best Chebyshev Approximations on Com
pacta 162
7.4. Some General Remarks on the Theory of Approximation
of Functions 164
Chapter III. Almost pebiodic Functions 170
§ 1. Uniform Almost periodic Functions on a Straight Line 170
1.1. Various Definitions of Almost periodic Functions 170
1.2. The Simplest Basic Properties of Almost periodic Func¬
tions 171
1.3. Fourier Series 172
1.4. Formal Operations on Fourier Series 175
1.5. Basic Theorems 176
1.6. The Approximation Theorem 178
1.7. The Convergence of Fourier Series for Some Classes of
Uniform Almost periodic Functions 179
CONTENTS Vii
1.8. The Relation Between the Fourier Exponents and Almost
periods 181
1.9. Kronecker s Theorem 182
1.10. Limited Periodic Functions 183
1.11. The Theorem of the Argument of a Uniform Almost periodic
Function 183
1.12. ^ almost periodic Functions 184
1.13. Linear Differential Equations with Almost periodic
Coefficients 186
§ 2. Various Generalizations of Almost periodic Functions 188
2.1. Introductory Remarks 188
2.2. The Definition and Simplest Properties of Stepanov Almost
periodic Functions 188
2.3. The Definition and Simplest Properties of Weyl Almost
periodic Functions 190
2.4. The Mean Value Theorem for TfP almost periodic functions.
Parseval s Equation for W2 and S^ almost periodic Func¬
tions. The Approximation Theorem 191
2.5. Besicovitch Almost periodic Functions 192
2.6. The Idea of Almost periodic Functions on Groups 193
§ 3. Analytic Almost periodic Functions 195
3.1. The Definition of Analytic Almost Periodic Functions and
Their Simplest Properties 195
3.2. Dirichlet Series 197
3.3. The Convergence of the Dirichlet Series for Analytic Almost
periodic Functions 199
3.4. The Behaviour of Almost periodic Functions when a = + oo
(analogues of the theorems of Weierstrass Sokhotskii and
Picard theorems) 199
3.5. Harmonic Almost periodic Functions 200
3.6. The Mean Movement and Density of Values of Analytic
Almost periodic Functions 201
References 206
Index op Symbols 209
Index 211
List ot Other Titles in the Semes 217
|
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| author | Guter, Rafail Samojlovič 1919-1978 Kudrjavcev, Lev Dmitrievič 1923-1984 Levitan, Boris M. 1914-2004 |
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| dewey-full | 517.5 |
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| dewey-search | 517.5 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. Engl. ed. |
| format | Book |
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| id | DE-604.BV003662462 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T08:08:11Z |
| institution | BVB |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002331378 |
| oclc_num | 251654933 |
| open_access_boolean | |
| owner | DE-384 DE-824 DE-91 DE-BY-TUM DE-29T DE-83 DE-188 |
| owner_facet | DE-384 DE-824 DE-91 DE-BY-TUM DE-29T DE-83 DE-188 |
| physical | XII, 219 S. graph. Darst. |
| publishDate | 1966 |
| publishDateSearch | 1966 |
| publishDateSort | 1966 |
| publisher | Pergamon Press |
| record_format | marc |
| series | International series of monographs in pure and applied mathematics |
| series2 | International series of monographs in pure and applied mathematics |
| spellingShingle | Guter, Rafail Samojlovič 1919-1978 Kudrjavcev, Lev Dmitrievič 1923-1984 Levitan, Boris M. 1914-2004 Elements of the theory of functions International series of monographs in pure and applied mathematics Fonctions (Mathématiques) Functions Funktionentheorie (DE-588)4018935-1 gnd |
| subject_GND | (DE-588)4018935-1 |
| title | Elements of the theory of functions |
| title_alt | Elementiy teorii funktsii |
| title_auth | Elements of the theory of functions |
| title_exact_search | Elements of the theory of functions |
| title_full | Elements of the theory of functions R. S. Guter, L. D. Kudryavtsev, B. M. Levitan |
| title_fullStr | Elements of the theory of functions R. S. Guter, L. D. Kudryavtsev, B. M. Levitan |
| title_full_unstemmed | Elements of the theory of functions R. S. Guter, L. D. Kudryavtsev, B. M. Levitan |
| title_short | Elements of the theory of functions |
| title_sort | elements of the theory of functions |
| topic | Fonctions (Mathématiques) Functions Funktionentheorie (DE-588)4018935-1 gnd |
| topic_facet | Fonctions (Mathématiques) Functions Funktionentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002331378&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001888024 |
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