Principles of Fourier analysis
Howell, Kenneth B.
Principles of Fourier analysis [recurso electrónico] / Kenneth B. Howell. - Boca Raton, Fla. : Chapman & Hall/CRC, c2001. - 1 online resource (776 p.) : ill. - Studies in advanced mathematics . - Studies in advanced mathematics. .
Includes bibliographical references (p. 757) and index.
The starting point -- Basic analysis I : continuity and smoothness -- Basic analysis II : integration and infinite series -- Symmetry and periodicity -- Elementary complex analysis -- Functions of several variables -- Heuristic derivation of the Fourier series formulas -- The trigonometric Fourier series -- Fourier series over finite intervals (sine and cosine series) -- Inner products, norms, and orthogonality -- The complex exponential Fourier series -- Convergence and Fourier's conjecture -- Convergence and Fourier's conjecture : the proofs -- Derivatives and integrals of Fourier series -- Applications -- Heuristic derivation of the classical Fourier transform -- Integrals on infinite intervals -- The Fourier integral transforms -- Classical Fourier transforms and classically transformable functions -- Some elementary identities : translation, scaling, and conjugation -- Differentiation and Fourier transforms -- Gaussians and other very rapidly decreasing functions -- Convolution and transforms of products -- Correlation, square-integrable functions, and the fundamental identity of Fourier analysis -- Identity sequences -- Generalizing the classical theory : a naive approach -- Fourier analysis in the analysis of systems -- Gaussians as test functions, and proofs of some important theorems -- A starting point for the generalized theory -- Gaussian test functions -- Generalized functions -- Sequences and series of generalized functions -- Basic transforms of generalized Fourier analysis -- Generalized products, convolutions, and definite integrals -- Periodic functions and regular arrays -- General solutions to simple equations and the pole function -- Periodic, regular arrays -- Sampling and the discrete Fourier transform. 1. 2. Basic terminology, notation, and conventions -- 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39.
1420036904 (electronic bk.) 9781420036909 (electronic bk.)
Fourier analysis.
Fourier, Analyse de.
MATHEMATICS--Infinity.
Fourier analysis.
Electronic books.
QA403.5 / .H69 2001
515/.2433
Principles of Fourier analysis [recurso electrónico] / Kenneth B. Howell. - Boca Raton, Fla. : Chapman & Hall/CRC, c2001. - 1 online resource (776 p.) : ill. - Studies in advanced mathematics . - Studies in advanced mathematics. .
Includes bibliographical references (p. 757) and index.
The starting point -- Basic analysis I : continuity and smoothness -- Basic analysis II : integration and infinite series -- Symmetry and periodicity -- Elementary complex analysis -- Functions of several variables -- Heuristic derivation of the Fourier series formulas -- The trigonometric Fourier series -- Fourier series over finite intervals (sine and cosine series) -- Inner products, norms, and orthogonality -- The complex exponential Fourier series -- Convergence and Fourier's conjecture -- Convergence and Fourier's conjecture : the proofs -- Derivatives and integrals of Fourier series -- Applications -- Heuristic derivation of the classical Fourier transform -- Integrals on infinite intervals -- The Fourier integral transforms -- Classical Fourier transforms and classically transformable functions -- Some elementary identities : translation, scaling, and conjugation -- Differentiation and Fourier transforms -- Gaussians and other very rapidly decreasing functions -- Convolution and transforms of products -- Correlation, square-integrable functions, and the fundamental identity of Fourier analysis -- Identity sequences -- Generalizing the classical theory : a naive approach -- Fourier analysis in the analysis of systems -- Gaussians as test functions, and proofs of some important theorems -- A starting point for the generalized theory -- Gaussian test functions -- Generalized functions -- Sequences and series of generalized functions -- Basic transforms of generalized Fourier analysis -- Generalized products, convolutions, and definite integrals -- Periodic functions and regular arrays -- General solutions to simple equations and the pole function -- Periodic, regular arrays -- Sampling and the discrete Fourier transform. 1. 2. Basic terminology, notation, and conventions -- 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39.
1420036904 (electronic bk.) 9781420036909 (electronic bk.)
Fourier analysis.
Fourier, Analyse de.
MATHEMATICS--Infinity.
Fourier analysis.
Electronic books.
QA403.5 / .H69 2001
515/.2433
