Approximation by polynomials composed of Weierstrass doubly periodic functions

Authors

  • Ksenia А. Sintsova HSE University, 16, ul. Soyuza Pechatnikov, StPetersburg, 190121, Russian Federation
  • Nikolay A. Shirokov HSE University, 16, ul. Soyuza Pechatnikov, StPetersburg, 190121, Russian Federation, St Petersburg State University, 7-9, Universitetskaya nab., St Petersburg, 199034, Russian Federation

DOI:

https://doi.org/10.21638/spbu01.2023.106

Abstract

The problem of describing classes of functions in terms of the rate of approximation of these functions by polynomials, rational functions, splines entered in the theory of approximation more than 100 years ago and still retains its relevance. Among a large number of problems related to approximation, we considered the problem of polynomial approximation in two variables of a function defined on the continuum of an elliptic curve in C2 and holomorphic in its interior. The formulation of such a question led to the need to study the approximation of a function that is continuous on the continuum of the complex plane and analytic in its interior, using polynomials in doubly periodic Weierstrass functions and their derivatives. This work is devoted to the development of this topic.

Keywords:

analytic functions, approximation, doubly periodic Weierstrass functions

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Published

2023-03-03

How to Cite

Sintsova K. А., & Shirokov, N. A. (2023). Approximation by polynomials composed of Weierstrass doubly periodic functions. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 10(1), 61–72. https://doi.org/10.21638/spbu01.2023.106

Issue

Vol. 10 No. 1 (2023)

Section

Mathematics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.