On the strong matrix summability of derived Fourier series.
On the strong summability and approximation of Fourier series
On the summability of Fourier series of functions of Λ-bounded variation
Periodic Boehmians.
Permitted trigonometric thin sets and infinite combinatorics
We investigate properties of permitted trigonometric thin sets and construct uncountable permitted sets under some set-theoretical assumptions.
Pointwise very strong approximation as a generalization of Fejér's summation theorem.
Randomly Weighted Series of Contractions in Hilbert Spaces.
Relationships between families of thin sets
Results on spline-Fourier and Ciesielski-Fourier series
Some recent results on spline-Fourier and Ciesielski-Fourier series are summarized. The convergence of spline Fourier series and the basis properties of the spline systems are considered. Some classical topics, that are well known for trigonometric and Walsh-Fourier series, are investigated for Ciesielski-Fourier series, such as inequalities for the Fourier coefficients, convergence a.e. and in norm, Fejér and θ-summability, strong summability and multipliers. The connection between Fourier series...
Riesz means of Fourier transforms and Fourier series on Hardy spaces
Elementary estimates for the Riesz kernel and for its derivative are given. Using these we show that the maximal operator of the Riesz means of a tempered distribution is bounded from to (1/(α+1) < p < ∞) and is of weak type (1,1), where is the classical Hardy space. As a consequence we deduce that the Riesz means of a function converge a.e. to ⨍. Moreover, we prove that the Riesz means are uniformly bounded on whenever 1/(α+1) < p < ∞. Thus, in case , the Riesz means converge...
Some footprints of Marcinkiewicz in summability theory
Four basic results of Marcinkiewicz are presented in summability theory. We show that setting out from these theorems many mathematicians have reached several nice results for trigonometric, Walsh- and Ciesielski-Fourier series.
Some negative results concerning the process of Fejér type trigonometric convolution.
Some remarks on a theorem of S.M. Lozinski concerning linear process of approximation of periodic functions
Stečkin inequalities for summability methods.
Suites lacunaires de Sidon, ensembles propres et points exceptionnels
Les ensembles “propres” pour une suite de Sidon sont caractérisés par une propriété de convergence des séries lacunaires à spectre dans la suite.
Summability of derived multiple Fourier series related to slowly oscillating functions with remainder term
Summability of generalized Fourier series and their conjugate series
The Banach Algebra A* and Its Problems.
The Gibbs phenomenon and Lebesgue constants for regular means
The structure of quasiasymptotics of Schwartz distributions
In this article complete characterizations of the quasiasymptotic behavior of Schwartz distributions are presented by means of structural theorems. The cases at infinity and the origin are both analyzed. Special attention is paid to quasiasymptotics of degree -1. It is shown how the structural theorem can be used to study Cesàro and Abel summability of trigonometric series and integrals. Further properties of quasiasymptotics at infinity are discussed. A condition for test functions in bigger spaces...