학술논문
Approximation of Riemann integrable functions by trigonometric convolution processes.
Document Type
Journal
Author
Mevissen, H. (D-AACH) AMS Author Profile; Nessel, R. J. (D-AACH) AMS Author Profile
Source
Subject
41 Approximations and expansions -- 41A Approximations and expansions
41A25Rate of convergence, degree of approximation
41A27Inverse theorems
42Harmonic analysis on Euclidean spaces -- 42A Harmonic analysis in one variable
42A10Trigonometric approximation
41A25
41A27
42
42A10
Language
English
Abstract
The authors continue their previous investigations concerning the approximation of Riemann integrable functions. For an enlarged error functional, Jackson-type estimates involving the $\tau$-modulus are derived as well as the corresponding inverse (Bernstein-type) theorems. Several concrete examples are discussed in the last sections.