On the summation of Fourier series

Summation of Fourier Series

A general summability method of different orthogonal series is given with the help of an integrable function θ. As special cases the trigonometric Fourier, Walsh-, Walsh-Kaczmarz-, Vilenkinand Ciesielski-Fourier series and the Fourier transforms are considered. For each orthonormal system a different Hardy space is introduced and the atomic decomposition of these Hardy spaces are presented. A s...

Summation of Multiple Fourier Series by Spherical Means.

Summation of Fourier

On the Summation of Certain Iterated Series

The paper gives a unified treatment of the summation of certain iterated series of the form ∑∞ n=1 ∑∞ m=1 an+m, where (an)n∈N is a sequence of real numbers. We prove that, under certain conditions, the double iterated series equals the difference of two single 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 ...