TY - BOOK ID - 46189011 TI - Functions of bounded variation and their Fourier transforms PY - 2019 SN - 3030044297 3030044289 PB - Cham : Springer International Publishing : Imprint: Birkhäuser, DB - UniCat KW - Functions of bounded variation. KW - Bounded variables, Functions of KW - Bounded variation, Functions of KW - BV functions KW - Functions of bounded variables KW - Functions of real variables KW - Harmonic analysis. KW - Abstract Harmonic Analysis. KW - Analysis (Mathematics) KW - Functions, Potential KW - Potential functions KW - Banach algebras KW - Calculus KW - Mathematical analysis KW - Mathematics KW - Bessel functions KW - Fourier series KW - Harmonic functions KW - Time-series analysis UR - https://www.unicat.be/uniCat?func=search&query=sysid:46189011 AB - 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. . ER -