Approximation of functions from B p, θ l (G) by anisotropic averages
The article considers the approximation of functions from O. V. Besov's class B p, θ l (G) by anisotropic average functions. Proofs are given of the approximation theorem, the inverse theorem of approximation theory, and the saturation theorem associated with the choice of the averaging kernel.
KeywordsAverage Function Approximation Theory Approximation Theorem Average Kernel Anisotropic Average
Unable to display preview. Download preview PDF.
- 1.O. V. Besov, “Investigating a family of functional spaces in connection with embedding and continuation theorems,” Tr. Mat. Inst. Akad. Nauk SSSR,60, 42–81 (1961).Google Scholar
- 2.O. V. Besov, V. P. Il'in, and S.M. Nikol'skii, Integral Representations of Functions and Embedding Theorems [in Russian], Moscow (1975).Google Scholar
- 3.K. K. Golovkin, “On approximation of functions in arbitrary norms,” Tr. Mat. Inst., Akad, Nauk SSSR,70, 26–37 (1964).Google Scholar
- 4.H. Shapiro, “Smoothing and approximation of functions,” Metsci. Report,55, 109 (1967).Google Scholar
- 5.S. M. Nikol'skii, Approximation of Functions of Many Variables and Embedding Theorems [in Russian], Moscow (1969).Google Scholar