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＜E-Book＞
Classical Fourier Transforms / by Komaravolu Chandrasekharan
(Universitext. ISSN:21916675)

Edition	1st ed. 1989.
Publisher	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Year	1989
Size	VII, 172 p : online resource
Authors	*Chandrasekharan, Komaravolu author SpringerLink (Online service)
Subjects	LCSH:Functions of real variables LCSH:Probabilities LCSH:Number theory FREE:Real Functions FREE:Probability Theory FREE:Number Theory
Notes	I. Fourier transforms on L1 (-?,?) -- §1. Basic properties and examples -- §2. The L1 -algebra -- §3. Differentiability properties -- §4. Localization, Mellin transforms -- §5. Fourier series and Poisson’s summation formula -- §6. The uniqueness theorem -- §7. Pointwise summability -- §8. The inversion formula -- §9. Summability in the L1-norm -- §10. The central limit theorem -- §11. Analytic functions of Fourier transforms -- §12. The closure of translations -- §13. A general tauberian theorem -- §14. Two differential equations -- §15. Several variables -- II. Fourier transforms on L2(-?,?) -- §1. Introduction -- §2. Plancherel’s theorem -- §3. Convergence and summability -- §4. The closure of translations -- §5. Heisenberg’s inequality -- §6. Hardy’s theorem -- §7. The theorem of Paley and Wiener -- §8. Fourier series in L2(a,b) -- §9. Hardy’s interpolation formula -- §10. Two inequalities of S. Bernstein -- §11. Several variables -- III. Fourier-Stieltjes transforms (one variable) -- §1. Basic properties -- §2. Distribution functions, and characteristic functions -- §3. Positive-definite functions -- §4. A uniqueness theorem -- Notes -- References HTTP:URL=https://doi.org/10.1007/978-3-642-74029-9

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