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Functions of Bounded Variation and Their Fourier Transforms - Elijah Liflyand

Functions of Bounded Variation and Their Fourier Transforms

(Autor)

Buch | Hardcover
XXIV, 194 Seiten
2019 | 1st ed. 2019
Springer International Publishing (Verlag)
978-3-030-04428-2 (ISBN)
CHF 164,75 inkl. MwSt
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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.   


Stock and tools.- Functions with derivative in a Hardy space.- Integrability spaces: wide, wider and widest.- Sharper results.- Stock and tools for several dimensions.- Integrability of the Fourier transforms.- Sharp results.- Bounded variation and discretization.- Multidimensional case: radial functions.

Erscheinungsdatum
Reihe/Serie Applied and Numerical Harmonic Analysis
Zusatzinfo XXIV, 194 p.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Gewicht 520 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Schlagworte asymptotic behavior • Bounded Variation • cosine and sine fourier transforms • Hardy space • hardy variation • Hilbert transform • integrability
ISBN-10 3-030-04428-9 / 3030044289
ISBN-13 978-3-030-04428-2 / 9783030044282
Zustand Neuware
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