Adyghe Int. Sci. J. Vol. 25, No. 2. Pp. 11–24.
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DOI: https://doi.org/10.47928/1726-9946-2025-25-2-11-24
EDN: BNTQAP
MATHEMATICS
| MSC 34A08, 34B05 | Original Article |
Approximation properties of the group of deviations
of periodic functions of two variables
Robert Andreevich Lasuriya
Doctor of Physical and Mathematical Sciences, Corresponding Member of the Academy of Sciences of Ukraine, Professor, Laureate of the State Prize named after G. A. Dzidzarya in the field of natural sciences, honored worker of the Higher School of the Republic of Abkhazia (Republic of Abkhazia, Sukhum, Universitetskaya street 1), ORCID: 0000-0003-2388-6070, rlasuria67@yandex.ru
Abstract. The paper continues the study of the rate of convergence of the group of deviations of rectangular sums of double trigonometric Fourier series, begun in [5]. The aim of the present article is to extend the results of [5] to the so-called generalized Lp-H¨older spaces Hω,p (T2), 1 ≤ p ≤ ∞, on the one hand, and to establish two-dimensional analogues of the author’s results [7] regarding the approximation properties of the group of deviations in generalized Lp-H¨older spaces of functions of one variable, on the other hand. The estimates established in the paper are of an ordinal nature and are formulated in terms of quantities defining the spaces Hω,p(T2)⊂Hω*,p (T2), and sequences α defining the corresponding groups of deviations.
Keywords: double Fourier series, Holder spaces,best approximation, modulus continuity.
Funding. The work was not carried out within the framework of funds.
Competing interests. There are no conflicts of interest regarding authorship and publication.
Contribution and Responsibility. The author participated in the writing of the article and is fully responsible for submitting the final version of the article to the press.
For citation. Lasuria R. A. Approximation properties of the group of deviations of periodic functions of two variables. Adyghe Int. Sci. J. 2025. Vol. 25, No. 2. Pp. 11–24.
DOI: https://doi.org/10.47928/1726-9946-2025-25-2-11-24; EDN: BNTQAP
Submitted 15.04.2025; approved after reviewing 03.06.2025; accepted for publication 07.06.2025.
© Lasuria R. A., 2025
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