A course in analysis: Vol. 4 Fourier analysis, ordinary differential equations, calculus of variations
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey, London, Singapore, Beijing, Shanghai, Hong Kong, Taipei, Chennai, Tokyo
World Scientific
[2018]
|
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xxvi, 742 Seiten Illustrationen |
| ISBN: | 9789813274525 9789813273511 |
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| 245 | 1 | 0 | |a A course in analysis |n Vol. 4 |p Fourier analysis, ordinary differential equations, calculus of variations |c Niels Jacob, Kristian P. Evans (Swansea University, UK) |
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Record in the Search Index
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| adam_text | Contents Preface v Introduction vii List of Symbols xix Part 8: Fourier Analysis 1 1 The Historical Place of Fourier Analysis in Mathematics 3 2 Trigonometric Series and Fourier Series 11 3 Fourier Series and Their Coefficients 27 4 Pointwise Convergence and Summability 47 5 Fourier Series of Square Integrable Functions 69 6 Further Topics on the Convergence of Fourier Series 87 7 Holomorphic Functions, Harmonic Functions, Hardy Spaces 105 8 Selected Topics on Fourier Series 123 9 Orthonormal Expansions and Special Functions 139 10 The Schwartz Space 157 11 The Fourier Transform in S(Rn) 173 12 The Fourier Transform in ZASpaces 191 13 The Fourier Transform of Bounded Measures 213 14 Selected Topics on the Fourier Transform 223 xv
A COURSE IN ANALYSIS Part 9: Ordinary Differential Equations 241 15 Some Orientation — First Results 243 16 Basic Existence and Uniqueness Results I 265 17 Basic Existence and Uniqueness Results II 283 18 Linear Systems of First Order. Constant Coefficients 291 19 Linear Systems of First Order. Variable Coefficients 315 20 Second Order Linear Differential Equations with Real Analytic Coefficients 335 21 Boundary Value and Eigenvalue Problems. First Observations 355 22 The Hypergeometric and the Confluent Hypergeometric Differential Equation 379 23 Continuous Dependence on Data and Stability 393 24 Tangent Spaces, Tangent Bundles, and Vector Fields 411 25 Phase Diagrams and Flows 429 Part 10: Introduction to the Calculus of Variations 445 26 The Calculus of Variations — Setting the Scene 447 27 Classical Solutions of the Euler-Lagrange Equations 467 28 More on Local Minimisers 483 29 Partial Differential Equations of 1st Order 497 30 Aspects of Hamilton-Jacobi Theory 523 XVI
CONTENTS Appendices 543 Appendix I: Harmonic Analysis on Locally Compact Abelian Groups 545 Appendix II: Convergence of Measures 565 Appendix III: Generating Functions, Orthonormal Polynomials 569 Appendix IV: On Brouwer’s Fixed Point Theorem 573 Solutions to Problems of Part 8 577 Solutions to Problems of Part 9 643 Solutions to Problems of Part 10 697 References 725 Mathematicians Contributing to Analysis (Continued) 733 Subject Index 735 xvii
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| id | DE-604.BV045250968 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:12:49Z |
| institution | BVB |
| isbn | 9789813274525 9789813273511 |
| language | English |
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| physical | xxvi, 742 Seiten Illustrationen |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | World Scientific |
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| spelling | Jacob, Niels 1955- Verfasser (DE-588)141510129 aut A course in analysis Vol. 4 Fourier analysis, ordinary differential equations, calculus of variations Niels Jacob, Kristian P. Evans (Swansea University, UK) New Jersey, London, Singapore, Beijing, Shanghai, Hong Kong, Taipei, Chennai, Tokyo World Scientific [2018] xxvi, 742 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Evans, Kristian P. Verfasser (DE-588)1163038571 aut (DE-604)BV043183538 4 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030638978&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jacob, Niels 1955- Evans, Kristian P. A course in analysis |
| title | A course in analysis |
| title_auth | A course in analysis |
| title_exact_search | A course in analysis |
| title_full | A course in analysis Vol. 4 Fourier analysis, ordinary differential equations, calculus of variations Niels Jacob, Kristian P. Evans (Swansea University, UK) |
| title_fullStr | A course in analysis Vol. 4 Fourier analysis, ordinary differential equations, calculus of variations Niels Jacob, Kristian P. Evans (Swansea University, UK) |
| title_full_unstemmed | A course in analysis Vol. 4 Fourier analysis, ordinary differential equations, calculus of variations Niels Jacob, Kristian P. Evans (Swansea University, UK) |
| title_short | A course in analysis |
| title_sort | a course in analysis fourier analysis ordinary differential equations calculus of variations |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030638978&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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