Sharp estimates for the convergence rate of Fourier series in terms of orthogonal polynomials in L 2((a, b), p(x)) |
| |
| Authors: | V. A. Abilov F. V. Abilova M. K. Kerimov |
| |
| Affiliation: | (1) Dagestan State University, ul. Gadzhieva 43a, Makhachkala, 367025, Russia;(2) Dagestan State Technical University, pr. Kalinina 70, Makhachkala, 367015, Russia;(3) Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia |
| |
| Abstract: | Sharp estimates are given for the convergence rate of Fourier series in terms of classical orthogonal polynomials in some classes of functions characterized by a generalized modulus of continuity in the space L 2((a, b), p(x)). Expansions in terms of Laguerre, Hermite, and Jacobi polynomials are considered. |
| |
| Keywords: | Fourier series generalized modulus of continuity width generalized derivatives expansions in terms of Laguerre, Hermite, Jacobi polynomials convergence of series |
| 本文献已被 SpringerLink 等数据库收录！ |
|
