Transformations of multiple Fourier series

Determination of a jump by Fourier and Fourier-Chebyshev series

‎By observing the equivalence of assertions on determining the jump of a‎ ‎function by its differentiated or integrated Fourier series‎, ‎we generalize a‎ ‎previous result of Kvernadze‎, ‎Hagstrom and Shapiro to the whole class of‎ ‎functions of harmonic bounded variation‎. ‎This is achieved without the finiteness assumption on‎ ‎the number of discontinuities‎. ‎Two results on determination of ...

Lebesgue Constants of Multiple Fourier Series

This is an attempt of a comprehensive treatment of the results concerning estimates of the L-norms of linear means of multiple Fourier series, the Lebesgue constants. Most of them are obtained by estimating the Fourier transform of a function generating such a method. Frequently the properties of the support of this function affects distinctive features in behavior of these norms. By this geome...

Transformations of Fourier Coefficients

Introduction. In 1923 M. Fekete [2]2 introduced the concept of factor sequences that left invariant the class of a Fourier series. That is, Fekete investigated the conditions to which a sequence of constants (X„) must be subjected in order that (X„a„, X„i„) be Fourier coefficients of a function of the same class, K, as that of the function determined by (an, bn). Whenever (X„) has this property...

Cesáro Means of N -multiple Trigonometric Fourier Series

Zhizhiashvili proved sufficient condition for the Cesáro summability by negative order of N-multiple trigonometric Fourier series in the space L, 1 ≤ p ≤ ∞. In this paper we show that this condition cannot be improved .

Summation of Multiple Fourier Series by Spherical Means.