Search

Your search keyword '"Tsagareishvili, Vakhtang"' showing total 33 results
Start Over Author "Tsagareishvili, Vakhtang"
33 results on '"Tsagareishvili, Vakhtang"'

2. Unconditional convergence of general Fourier series

Author

Tsagareishvili, Vakhtang, Tutberidze, Giorgi, and Cagareishvili, Giorgi

Subjects
Mathematics - Functional Analysis
Abstract

S. Banach, in particular, proved that for any function, even $f(x) = 1,$ where $x\in[0,1],$ the convergence of its Fourier series with respect to the general orthonormal systems (ONS) is not guaranteed. In this paper, we find conditions for the functions $\varphi_{n}$ of an ONS $(\varphi_n),$ under which the Fourier series of functions $f\in Lip_1$ are unconditionally convergent almost everywhere. During our research, we mainly used the properties of the sequences of linear functionals on the Banach spaces to prove the main theorems we presented in this article. Our research has concluded that the aforementioned conditions do exist and are the best possible in a certain sense. We have also found that any ONS contains a subsystem such that the Fourier series of any function $f\in Lip_1$ is unconditionally convergent. Further, the precondition presented in Theorem \ref{theorem1.1}, which demands that the Fourier series of the function $f=1$ be convergent, is adequate, meaning that it does not make the actual conditions of Theorem \ref{theorem1.1} redundant. We have shown that the solution for these types of problems for the general ONS is trivial for the classical ONS (trigonometric, Haar, and Walsh systems).

Published
2023

10. Absolute convergence factors of Lipschitz class functions for general Fourier series.

Author

Tsagareishvili, Vakhtang and Tutberidze, Giorgi

Subjects
*FOURIER series, *SPECIAL functions, *LIPS
Abstract

The main aim of this paper is to investigate the sequences of positive numbers, for which multiplication with Fourier coefficients of functions f ∈ Lip ⁡ 1 {f\in\operatorname{Lip}1} class provides absolute convergence of Fourier series. In particular, we found special conditions for the functions of orthonormal system (ONS), for which the above sequences are absolute convergence factors of Fourier series of functions of Lip ⁡ 1 {\operatorname{Lip}1} class. It is established that the resulting conditions are best possible in certain sense. [ABSTRACT FROM AUTHOR]

Published
2022
Full Text
View/download PDF

Catalog

Books, media, physical & digital resources
See catalog results