Principles of Fourier analysis [recurso electrónico] / Kenneth B. Howell.
Tipo de material: TextoSeries Studies in advanced mathematicsDetalles de publicación: Boca Raton, Fla. : Chapman & Hall/CRC, c2001Descripción: 1 online resource (776 p.) : illISBN: 1420036904 (electronic bk.); 9781420036909 (electronic bk.)Tema(s): Fourier analysis | Fourier, Analyse de | MATHEMATICS -- Infinity | Fourier analysisGénero/Forma: Electronic books.Formatos físicos adicionales: Print version:: Principles of Fourier analysis.Clasificación CDD: 515/.2433 Clasificación LoC:QA403.5 | .H69 2001Recursos en línea: Libro electrónicoTipo de ítem | Biblioteca actual | Colección | Signatura | Copia número | Estado | Fecha de vencimiento | Código de barras |
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Libro Electrónico | Biblioteca Electrónica | Colección de Libros Electrónicos | QA403.5 .H69 2001 (Browse shelf(Abre debajo)) | 1 | No para préstamo | 369722-2001 |
Navegando Biblioteca Electrónica Estantes, Código de colección: Colección de Libros Electrónicos Cerrar el navegador de estanterías (Oculta el navegador de estanterías)
QA403 -403.3 Four Short Courses on Harmonic Analysis | QA403 -403.3 Harmonic Analysis of Operators on Hilbert Space | QA403 -403.3 Convolution Operators on Groups | QA403.5 .H69 2001 Principles of Fourier analysis | QA403.5 .K36 2007 EB A first course in fourier analysis | QA403.5 -404.5 Wavelets and Multiscale Analysis | QA403.5 -404.5 Fourier Integral Operators |
Includes bibliographical references (p. 757) and index.
1. The starting point -- 2. Basic terminology, notation, and conventions -- 3. Basic analysis I : continuity and smoothness -- 4. Basic analysis II : integration and infinite series -- 5. Symmetry and periodicity -- 6. Elementary complex analysis -- 7. Functions of several variables -- 8. Heuristic derivation of the Fourier series formulas -- 9. The trigonometric Fourier series -- 10. Fourier series over finite intervals (sine and cosine series) -- 11. Inner products, norms, and orthogonality -- 12. The complex exponential Fourier series -- 13. Convergence and Fourier's conjecture -- 14. Convergence and Fourier's conjecture : the proofs -- 15. Derivatives and integrals of Fourier series -- 16. Applications -- 17. Heuristic derivation of the classical Fourier transform -- 18. Integrals on infinite intervals -- 19. The Fourier integral transforms -- 20. Classical Fourier transforms and classically transformable functions -- 21. Some elementary identities : translation, scaling, and conjugation -- 22. Differentiation and Fourier transforms -- 23. Gaussians and other very rapidly decreasing functions -- 24. Convolution and transforms of products -- 25. Correlation, square-integrable functions, and the fundamental identity of Fourier analysis -- 26. Identity sequences -- 27. Generalizing the classical theory : a naive approach -- 28. Fourier analysis in the analysis of systems -- 29. Gaussians as test functions, and proofs of some important theorems -- 30. A starting point for the generalized theory -- 31. Gaussian test functions -- 32. Generalized functions -- 33. Sequences and series of generalized functions -- 34. Basic transforms of generalized Fourier analysis -- 35. Generalized products, convolutions, and definite integrals -- 36. Periodic functions and regular arrays -- 37. General solutions to simple equations and the pole function -- 38. Periodic, regular arrays -- 39. Sampling and the discrete Fourier transform.
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