相关论文: On L1 Convergence of Fourier Series of Complex Val…
It is proved that the complex double Fourier series of an integrable function $f(x,y)$ with coefficients $\{c_{jk}\}$ satisfying certain conditions, will converge in $L^{1}$-norm. The conditions used here are the combinations of Tauberian…
In the present paper we consider the trigonometric series with (b,r)-general monotone and (b,r)-rest bounded variation coefficients. Necessary and sufficien conditions of L-convergence for such series are obtained in terms of the…
The paper introduces a new concept of $\Lambda $-variation of multivariable functions and investigates its connection with the convergence of multidimensional Fourier series
We give a transform of convergent trigonometric series into equivalent convergent series and sufficient conditions for the transformed series to converge faster than the original one.
A trigonometric series strongly bounded at two points and with coefficients forming a log-quasidecreasing sequence is necessarily the Fourier series of a function belonging to all $L^{p}$ spaces, $1\leq p < \infty$. We obtain new results on…
We note that the Fubini theorem may be used to prove that an $L^1$ function is determined by its Fourier coefficients.
The convergence of multiple Fourier series of functions of bounded partial $% \Lambda$-variation is investigated. The sufficient and necessary conditions on the sequence $\Lambda=\{\lambda_n\}$ are found for the convergence of multiple…
In this paper we obtain degree of approximation of functions in Lp by operators associated with their Fourier series using integral modulus of continuity. These results generalize many know results and are proved under less stringent…
In this note we consider the Fourier expansion of the Ferrers function P of the first kind. We determine its mode of convergence.
The convergence of double Fourier series of functions of bounded partial $\Lambda$-variation is investigated. The sufficient and necessary conditions on the sequence $\Lambda=\{\lambda_n\}$ are found for the convergence of Fourier series of…
In this paper we present results on convergence and Ces\`{a}ro summability of Multiple Fourier series of functions of bounded generalized variation.
In this paper we discuss some convergence and divergence properties of subsequences of logarithmic means of Walsh-Fourier series . We give necessary and sufficient conditions for the convergence regarding logarithmic variation of numbers.
In this paper we consider a transformation $L_a$ of sequences of complex numbers. We find the inverse transformation of $L_a$ as well as the inverse of a related transformation $\tilde{L}_a$. We explore a connection to the binomial…
The main aim of this paper is to investigate the sequences of positive numbers, for which multiplication with Fourier coefficients of functions $f\in$ Lip1 class provides absolute convergence of Fourier series. In particular we found…
The author's method (math-ph/9804010) that uses the Laplace transform to find exact values for a large class of convergent series is extended to trigonometric series.
In this paper we consider trigonometric series with p-bounded variation coefficients. We presented a sufficient condition for uniform convergance of such series in case p > 1. This condition is significantly weaker than these obtained in…
We introduce an amalgam type space, a subspace of $L^1(\mathbb R_+).$ Integrability results for the Fourier transform of a function with the derivative from such an amalgam space are proved. As an application we obtain estimates for the…
In this paper, we investigate the convergence properties of Fourier partial sums associated with general orthonormal systems, focusing on functions that belong to specific differentiable function classes. While classical Fourier analysis…
The main object of the present paper is to give a complete result regarding the best approximation rate of certain trigonometric series in general complex valued continuous function space under a new condition which gives an essential…
A correspondence between arbitrary Fourier series and certain analytic functions on the unit disk of the complex plane is established. The expression of the Fourier coefficients is derived from the structure of complex analysis. The…