Early fourier analysis:
Gespeichert in:
1. Verfasser: | |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2014]
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Schriftenreihe: | Pure and applied undergraduate texts
22 |
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | X, 390 Seiten Diagramme 27 cm |
ISBN: | 9781470415600 1470415607 |
Internformat
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Datensatz im Suchindex
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adam_text | Titel: Early Fourier analysis
Autor: Montgomery, Hugh L
Jahr: 2014
Pure UNDERGRADUATE Early Fourier Analysis Hugh L.^Montgomery American Mathematical Society Providence, Rhode Island
Contents Preface ix Chapter 0. Background 1 0.1. Elementary mathematics 1 0.2. Real analysis 3 0.3. Lebesgue measure theory 7 Chapter 1. Complex Numbers 9 1.1. Basics 9 1.2. Euclidean geometry via complex numbers 13 1.3. Polynomials 17 1.4. Power series 21 Notes 31 Chapter 2. The Discrete Fourier Transform 33 2.1. Sums of roots of unity 33 2.2. The Transform 36 2.3. The Fast Fourier Transform 48 Notes 51 Chapter 3. Fourier Coefficients and First Fourier Series 53 3.1. Definitions and basic properties 53 3.2. Other periods 68 3.3. Convolution 69 3.4. First Convergence Theorems 75 Notes 88 v
VI Contents Chapter 4. Summability of Fourier Series 91 4.1. Cesàro summability of Fourier Series 91 4.2. Special coefficients 111 4.3. Summability 120 4.4. Summability kernels 130 Notes 134 Chapter 5. Fourier Series in Mean Square 135 5.1. Vector spaces of functions 135 5.2. Parseval’s Identity 138 Notes 148 Chapter 6. Trigonometric Polynomials 149 6.1. Sampling and interpolation 149 6.2. Bernstein’s Inequality 158 6.3. Real-valued and nonnegative trigonometric polynomials 162 6.4. Littlewood polynomials 165 6.5. Quantitative approximation of continuous functions 175 Notes 182 Chapter 7. Absolutely Convergent Fourier Series 183 7.1. Convergence 183 7.2. Wiener’s theorem 191 Notes 194 Chapter 8. Convergence of Fourier Series 195 8.1. Conditions ensuring convergence 195 8.2. Functions of bounded variation 198 8.3. Examples of divergence 205 Notes 209 Chapter 9. Applications of Fourier Series 211 9.1. The heat equation 211 9.2. The wave equation 213 9.3. Continuous, nowhere differentiable functions 215 9.4. Inequalities 217 9.5. Bernoulli polynomials 220 9.6. Uniform distribution 229 9.7. Positive definite kernels 239 9.8. Norms of polynomials 241 Notes 246
Contents vii Chapter 10. The Fourier Transform 249 10.1. Definition and basic properties 249 10.2. The inversion formula 255 10.3. Fourier transforms in mean square 263 10.4. The Poisson summation formula 270 10.5. Linear combinations of translates 277 Notes 278 Chapter 11. Higher Dimensions 279 11.1. Multiple Discrete Fourier Transforms 279 11.2. Multiple Fourier Series 280 11.3. Multiple Fourier Transforms 286 Notes 290 Appendix B. The Binomial Theorem 291 B.l. Binomial coefficients 291 B.2. Binomial theorems 293 Appendix C. Chebyshev Polynomials 299 Appendix F. Applications of the Fundamental Theorem of Algebra 309 F.l. Zeros of the derivative of a polynomial 309 F.2. Linear differential equations with constant coefficients 312 F.3. Partial fraction expansions 313 F.4. Linear recurrences 315 Appendix I. Inequalities 319 1.1. The Arithmetic-Geometric Mean Inequality 319 1.2. Holder’s Inequality 325 Notes 338 Appendix L. Topics in Linear Algebra 339 L.l. Familiar vector spaces 339 L.2. Abstract vector spaces 344 L.3. Circulant matrices 347 Notes 348 Appendix O. Orders of Magnitude 349 Appendix T. Trigonometry 351 T.l. Trigonometric functions in plane geometry 351 T.2. Trigonometric functions in calculus 357
Contents viii T.3. Inverse trigonometric functions 364 T.4. Hyperbolic functions 369 References 377 Notation 383 Index 385
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any_adam_object | 1 |
author | Montgomery, Hugh L. 1944- |
author_GND | (DE-588)172262968 |
author_facet | Montgomery, Hugh L. 1944- |
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author_sort | Montgomery, Hugh L. 1944- |
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building | Verbundindex |
bvnumber | BV042319253 |
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contents | Includes bibliographical references and index |
ctrlnum | (OCoLC)906057607 (DE-599)BVBBV042319253 |
dewey-full | 515.2433 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 515 - Analysis |
dewey-raw | 515.2433 |
dewey-search | 515.2433 |
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dewey-tens | 510 - Mathematics |
discipline | Mathematik |
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indexdate | 2024-07-10T01:18:19Z |
institution | BVB |
isbn | 9781470415600 1470415607 |
language | English |
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physical | X, 390 Seiten Diagramme 27 cm |
publishDate | 2014 |
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publishDateSort | 2014 |
publisher | American Mathematical Society |
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series | Pure and applied undergraduate texts |
series2 | Pure and applied undergraduate texts The Sally series |
spelling | Montgomery, Hugh L. 1944- Verfasser (DE-588)172262968 aut Early fourier analysis Hugh L. Montgomery Providence, Rhode Island American Mathematical Society [2014] © 2014 X, 390 Seiten Diagramme 27 cm txt rdacontent n rdamedia nc rdacarrier Pure and applied undergraduate texts 22 The Sally series Includes bibliographical references and index Harmonic analysis Fourier transformations Harmonic analysis on Euclidean spaces / Instructional exposition (textbooks, tutorial papers, etc.) msc Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Fourier-Transformation (DE-588)4018014-1 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 s Fourier-Transformation (DE-588)4018014-1 s DE-604 Pure and applied undergraduate texts 22 (DE-604)BV035489189 22 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027756220&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Montgomery, Hugh L. 1944- Early fourier analysis Pure and applied undergraduate texts Includes bibliographical references and index Harmonic analysis Fourier transformations Harmonic analysis on Euclidean spaces / Instructional exposition (textbooks, tutorial papers, etc.) msc Harmonische Analyse (DE-588)4023453-8 gnd Fourier-Transformation (DE-588)4018014-1 gnd |
subject_GND | (DE-588)4023453-8 (DE-588)4018014-1 |
title | Early fourier analysis |
title_auth | Early fourier analysis |
title_exact_search | Early fourier analysis |
title_full | Early fourier analysis Hugh L. Montgomery |
title_fullStr | Early fourier analysis Hugh L. Montgomery |
title_full_unstemmed | Early fourier analysis Hugh L. Montgomery |
title_short | Early fourier analysis |
title_sort | early fourier analysis |
topic | Harmonic analysis Fourier transformations Harmonic analysis on Euclidean spaces / Instructional exposition (textbooks, tutorial papers, etc.) msc Harmonische Analyse (DE-588)4023453-8 gnd Fourier-Transformation (DE-588)4018014-1 gnd |
topic_facet | Harmonic analysis Fourier transformations Harmonic analysis on Euclidean spaces / Instructional exposition (textbooks, tutorial papers, etc.) Harmonische Analyse Fourier-Transformation |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027756220&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
volume_link | (DE-604)BV035489189 |
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