Related papers: Convergence and Summability of Multiple Fourier se…
The convergence of partial sums and Ces\'aro means of negative order of double Walsh-Fourier series of functions of bounded \ generalized variation is investigated.
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…
The paper introduces a new concept of $\Lambda $-variation of multivariable functions and investigates its connection with the convergence of multidimensional Fourier series
An analogue of D. Waterman's result on the summability of the Fourier series for functions of bounded \Lambda-variation by the Ces\'aro methods of negative order is obtained in multidimensional case. It is proved that, unlike…
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…
The convergence of Ces\`{a}ro means of negative order of double trigonometric Fourier series of functions of bounded partial $\Lambda$-variation is investigated. The sufficient and neccessary conditions on the sequence $\Lambda…
The Uniform convergence of double Fourier-Legendre series of function of bounded Harmonic variation and bounded partial $\Lambda $-variation are investigated.
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 investigate the summability in sense of Cesaro and its applications to investigation of the mean values of multiplicative functions on permutations.
The conditions for convergence of square and rectangular Fejer means of functions on the infinite dimensional torus were obtained, also a generalization of the results for the case of abstract measure spaces was formulated.
The article studies the convergence of trigonometric Fourier series via a new Tauberian theorem for Ces\`{a}ro summable series in abstract normed spaces. This theorem generalizes some known results of Hardy and Littlewood for number series.…
In this paper, we investigate the Ces\'aro means of Fourier series with respect to general orthonormal systems (ONS), when the function \( f \) belongs to a certain differentiable class of functions. It is well known that the membership of…
In this paper we investigate some convergence and divergence properties of the logarithmic means of quadratical partial sums of double Fourier series of functions in the measure and in the $L$ Lebesgue norm.
In the present paper, we give a brief review of $L^{1}$-convergence of trigonometric series. Previous known results in this direction are improved and generalized by establishing a new condition.
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…
We investigate a result on convergence of double sequences of numbers and how it extends to measurable functions.
A result concerning the Ces\`aro summability of the Fourier orthogonal expansion of a function on the cylinder, where the orthogonal basis consists of orthogonal polynomials, in the $L^p$ norms is presented. An upper bound for critical…
It is shown that quasi all continuous functions on the unit circle have the property that, for many small subsets E of the circle, the partial sums of their Fourier series considered as functions restricted to E exhibit certain universality…
We introduce semicontinuous summation methods for series of fuzzy numbers and give Tauberian conditions under which summation of a series of fuzzy numbers via generalized Dirichlet series and via generalized factorial series implies its…
This is the first in a set of three papers providing an introduction to generalised Cesaro convergence. We start with traditional Cesaro methods for extending classical convergence and further generalise these to allow the calculation of…