Functions of Bounded Variation and Their Fourier Transforms (Applied and Numerical Harmonic Analysis) - Hardcover

Liflyand, Elijah

Hardcover

ISBN 10: 3030044289 ISBN 13: 9783030044282

Verlag: Birkhäuser, 2019

Inhaltsangabe

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.   

Über diesen Titel

Über die Autorin bzw. den Autor

Elijah Liflyand has recently retired from his position at the Department of Mathematics at Bar-Ilan University in Israel, but not from mathematics. He also holds a position at the at the Regional Mathematical Center of Southern Federal University in Rostov-on-Don, Russia. His areas of expertise are in Fourier Analysis, Complex Analysis, and Approximation Theory, among others. With Birkhäuser/Springer, he has published two books: "Decay of the Fourier Transform" (with Alex Iosevich, 2014), and "Functions of Bounded Variation and Their Fourier Transforms" (in the Applied Numerical and Harmonic Analysis series, 2019).

Von der hinteren Coverseite

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.   

Details zur Ausgabe

• Verlag: Birkhäuser
• Erscheinungsdatum: 2019
• Sprache: Englisch
• ISBN 10: 3030044289
• ISBN 13: 9783030044282
• Einband: Gebundene Ausgabe
• Auflage: 1
• Anzahl der Seiten: 218
• Kontakt zum Hersteller: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Deutschland