2017
Том 69
№ 9

All Issues

Determination of jumps in terms of linear operators

Zviadadze Sh.


Abstract

A theorem of Luk´acs [4] states that the partial sums of conjugate Fourier series of a periodic Lebesgue integrable function $f$ diverge with a logarithmic rate at the points of discontinuity of $f$ of the first kind. M´oricz [5] proved a similar theorem for the rectangular partial sums of double variable functions.
We consider analogs of the M´oricz theorem for generalized Ces´aro means and for positive linear means.
We consider a similar theorem in terms of linear operators satisfying certain conditions.

Citation Example: Zviadadze Sh. Determination of jumps in terms of linear operators // Ukr. Mat. Zh. - 2015. - 67, № 12. - pp. 1649-1657.