Functions of bounded variation and their fourier transforms [Documento eletrónico] / by Elijah Liflyand
Language: eng.Country: Switzerland, Swiss Confederation.Publication: Cham : Springer International Publishing, Birkhäuser, 2019Description: XXIV, 194 p.ISBN: 978-3-030-04429-9.Series: Applied and Numerical Harmonic AnalysisSubject - Topical Name: Harmonic analysis Online Resources:Click here to access onlineItem type | Current library | Collection | Call number | Copy number | Status | Date due | Barcode | |
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E-Books | Biblioteca NOVA FCT Online | Não Ficção | QA403.SPR FCT (Browse shelf(Opens below)) | 1 | Available | 96001 |
Functions of bounded variation represent an important class of functions. Studying their Fourier transforms is a valuable means of revealing their analytic properties. Moreover, it brings to light new interrelations between these functions and the real Hardy space and, correspondingly, between the Fourier transform and the Hilbert transform. This book is divided into two major parts, the first of which addresses several aspects of the behavior of the Fourier transform of a function of bounded variation in dimension one. In turn, the second part examines the Fourier transforms of multivariate functions with bounded Hardy variation. The results obtained are subsequently applicable to problems in approximation theory, summability of the Fourier series and integrability of trigonometric series. .
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