EAN: 9783030044282

FUNCTIONS OF BOUNDED VARIATION AND THEIR FOURIE...

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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