The absolute convergence of the Fourier-Haar series for two-dimensional functions |
| |
Authors: | L. D. Gogoladze V. Sh. Tsagareishvili |
| |
Affiliation: | (1) Tbilisi State University, pr. Chavchavadze 1, Tbilisi, 380028, Georgia |
| |
Abstract: | It is well-known that if an one-dimensional function is continuously differentiable on [0, 1], then its Fourier-Haar series converges absolutely. On the other hand, if a function of two variables has continuous partial derivatives f x ′ and f y ′ on T 2, then its Fourier series does not necessarily absolutely converge with respect to a multiple Haar system (see [1]). In this paper we state sufficient conditions for the absolute convergence of the Fourier-Haar series for two-dimensional continuously differentiable functions. |
| |
Keywords: | absolute convergence Fourier series Haar system functions of two variables Rademacher system convergence almost everywhere |
本文献已被 SpringerLink 等数据库收录! |