Generalized translation operator and approximation in several variables

Details Generalized translation operator and approximation in several variables Generalized translation operator and approximation in several variables

2004-01-29

arxiv.org/abs/math/0401417v1

Mathematics

Classical Analysis and ODEs

22 pages, 7th International Symposium on Orthogonal Polynomials and Special Functions, Copenhagen, August 2003

Scientific paper

Generalized translation operators for orthogonal expansions with respect to families of weight functions on the unit ball and on the standard simplex are studied. They are used to define convolution structures and modulus of smoothness for these regions, which are in turn used to characterize the best approximation by polynomials in the weighted $L^p$ spaces. In one variable, this becomes the generalized translation operator for the Gegenbauer polynomial expansions.

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