Vilenkin system

On Weighted Analogs of Wiener’s and Levy’s Theorems for Fourier – Vilenkin Series

Authors: Volosivets S. S.

In this paper we find the general form of complex homomorphism for some subalgebras of absolutely convergent Fourier – Vilenkin series algebra. As a corollary, we obtain weighted analogs of Wiener’s and Levy’s theorems for Fourier – Vilenkin series.

Several Questions of Approximation by Polynomials with Respect to Multiplicative Systems in Weighted Lp Spaces

Authors: Volosivets S. S., Likhacheva T. V.

In this paper we study approximation by Vilenkin polynomials in weighted Lp spaces. We prove the Butzer – Scherer type result on equivalence between the rate of best approximation of a function f and the growth of generalized derivatives and approximating properties of the best approximation polynomial tn(f). Some applications to the approximation by linear means of the Fourier – Vilenkin series are given.

Approximation of Functions in Symmetrical and Connected Holder Spaces by Linear Means of Fourier–Vilenkin Series

Authors: Likhacheva T. V.

In this paper some summation methods are applied to Fourier-Vilenkin series in so called symmetric spaces. These methods use triangular matrix with sums in rows tending to zero and with some conditions on difference of coefficients. The triginometric counterpart of our results are due to M. L. Mittal, B. E. Rhoades, A. Guven, etc.