M. L. Kazarian, “Regularized summation of Haar series of continuous functions”, Vladikavkaz. Mat. Zh., 2016, Volume 18, Number 2,Pages <nobr>49

Regularized summation of Haar series of continuous functions

M. L. Kazarian^ab

^a North Ossetian State University after Kosta Levanovich Khetagurov, Vladikavkaz, Russia
^b Financial University under the Government of the Russian Federation, Vladikavkaz Branch, Vladikavkaz, Russia

Abstract: We study the problem of summation of Haar series of continuous functions. We present the proof of the stability and uniform convergence of Haar series regularized by generalized summation function for the class of continuous functions with approximate coefficients.

Key words: Haar transformation, Haar series, Tikhonov regularization method, regularizing multiplier, class of functions $S_p$, $1\leq p<\infty$.

UDC: 004.934

Received: 10.07.2014