Principles of Fourier analysis [recurso electrónico] / Kenneth B. Howell.

Por: Howell, Kenneth BTipo de material: TextoTextoSeries 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 electrónicoTexto
Contenidos:
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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Existencias
Tipo de ítem Biblioteca actual Colección Signatura Copia número Estado Fecha de vencimiento Código de barras
Libro Electrónico Biblioteca Electrónica
Colección de Libros Electrónicos QA403.5 .H69 2001 (Browse shelf(Abre debajo)) 1 No para préstamo 369722-2001

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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