Sharp estimates for the rate of convergence of double Fourier series in classical orthogonal polynomials

Autor:	M. K. Kerimov, V. A. Abilov, M. V. Abilov
Rok vydání:	2015
Předmět:	Classical orthogonal polynomials Computational Mathematics Hermite polynomials Rate of convergence Mathematical analysis Laguerre polynomials Differentiable function Shift operator Fourier series Modulus of continuity Mathematics
Zdroj:	Computational Mathematics and Mathematical Physics. 55:1094-1102
ISSN:	1555-6662 0965-5425
DOI:	10.1134/s0965542515070027
Popis:	Sharp estimates are obtained for the convergence rate of “triangular” and “hyperbolic” partial sums of Fourier series in orthogonal (Laguerre, Hermite, Jacobi) polynomials in the classes of differentiable functions of two variables characterized by a generalized modulus of continuity. The proofs are based on the generalized shift operator and generalized modulus of continuity for functions from L2 having generalized partial derivatives in Levi’s sense.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::c67557a6d9f1a6c6d9e9b15aad28c79c https://doi.org/10.1134/s0965542515070027 Zobrazit plný text záznamu Full text from SpringerLink