Determination of jumps in terms of linear operators
AbstractA theorem of Luk´acs  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  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.
How to Cite
Zviadadze, S. “Determination of Jumps in Terms of Linear Operators”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, no. 12, Dec. 2015, pp. 1649-57, https://umj.imath.kiev.ua/index.php/umj/article/view/2097.