arXiv subjects

Wlodzimierz Lenski

Publications and source records attributed to Wlodzimierz Lenski.

8 recordsLinked to original sources

arXiv2019

Pointwise strong (H, Phi) approximation by Fourier series of L^{Psi} integrable functions

We essentially extend and improve the classical result of G. H. Hardy and J. E. Littlewood on strong summability of Fourier series. We will present an estimation of the generalized strong mean (H; Phi) as an approximation version of the Totik type generalization of the result of G. H. Hardy, J. E. Littlewood, in case of integrable functions from L^{Psi}. As a measure of such approximation we will use the function constructed by function Psi complementary to Phi on the base of defnition of the L^{Psi} points. Some corollary and remarks will also be given.

math.CA↗

arXiv2019

Pointwise summability of Fourier-Laguerre series of integrable functions

We present an approximation version of the results of D. P. Gupta [ J. of Approx. Theory, 7 (1973), 226-238] A. N. S. Singroura [Proc. Japan Acad., 39 (4) (1963), 208-210] and G. Szegö [Math. Z., 25 (1926), 87-115]. Some corollaries and examples will also be given.

math.CA↗

arXiv2019

Estimates of convolution operators of functions from $L_{2π}^{p(x)}$

We generalize and slight improve the result of I. I. Sharapudinov [Mat. Zametki, 1996, Volume 59, Issue 2, 291--302]. Some applications to the de la Vallée Poussin operator will also be given.

math.CA↗

arXiv2019

On estimates of deviation of conjugate functions from matrix operators of their Fourier series by some expressions with $r$-differences of the entries

We extend the results of the authors from [Abstract and Applied Analysis, Volume 2016, Article ID 9712878] to the case conjugate Fourier series.

math.CA↗

arXiv2019

Pointwise approximation of functions by matrix operators of their Fourier series with $r$- differences of the entries

We extend the results of Xh. Z. Krasniqi [Acta Comment. Univ. Tartu. Math. 17 (2013), 89-101] and the authors [Acta Comment. Univ. Tartu. Math. 13 (2009), 11-24]. to the case where in the measures of estimations there are used $r$-differences of the entries.

math.CA↗

arXiv2014

Approximation of conjugate functions by general linear operators of their Fourier series at the Lebesgue points

The pointwise estimates of the deviations $\widetilde{T}_{n,A,B}^{\text{}%}f\left(\cdot \right) -\widetilde{f}(\cdot)$ and $\widetilde{T}_{n,A,B}^{% \text{}}f\left(\cdot \right) -\widetilde{f}(\cdot,\varepsilon)$ in terms of moduli of continuity $\widetilde{\bar{w}}_{\cdot}f$ and $\widetilde{w}%_{\cdot}f$ are proved. Analogical results on norm approximation with remarks and corollary are also given. These results generalized a theorem of Mittal.

math.AP↗

arXiv2012

Pointwise strong approximation of almost periodic functions in S^1

We consider the class GM(2b) in pointwise estimate of the deviations in strong mean of S^1 almost periodic functions from matrix means of partial sums of their Fourier series.

math.CA↗

arXiv2012

On the degree of strong approximation of almost periodic functions in the Stepanov sense

Considering the class of almost periodic functions in the Stepanov sense we extend and generalize the results of the first author [4]. as well as the results of L. Leindler [3] and P. Chandra [1,2].

math.CA↗