Work

Approximation by Subsequences of Matrix Transform Means of Some Two-Dimensional Rectangle Walsh–Fourier Series

Year: 2024

Type: article

Abstract: In the present paper we discuss the rate of the approximation by the matrix transform of special partial sums of some two-dimensional rectangle (decreasing diagonal) Walsh-Fourier series in $$L^p(G^{2})$$ L p ( G 2 ) space ( $$1\le p <\infty $$ 1 ≤ p < ∞ ) and in $$C(G^{2})$$ C ( G 2 ) . It implies in some special case "Equation missing"norm convergence. We also show an application of our results for Lipschitz functions. At the end of the paper we show the most important result, the almost everywhere convergence theorem. We note that T summation is a common generalization of the following known summation methods Cesàro, Weierstrass, Riesz and Picar and Bessel methods.

Source: Journal of Fourier Analysis and Applications

DOI: 10.1007/s00041-024-10106-x

Authors: István Blahota, György Gát

Institutions: University of Nyíregyháza, University of Debrecen

Language: English

Topic: Approximation Theory and Sequence Spaces

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,890

Funder: Debreceni Egyetem