Generalized translation operator and approximation in several variables
Copyright policy )Generalized translation operator and approximation in several variables
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.
22 pages, 7th International Symposium on Orthogonal Polynomials and Special Functions, Copenhagen, August 2003
- University of Oregon United States
- University of Oregon Eugene United States
Applied Mathematics, Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable, Multidimensional problems, General harmonic expansions, frames, Modulus of smoothness, Approximation by other special function classes, \(K\)-functional, Computational Mathematics, Several variables, modulus of smoothness, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Best approximation, Translation operator, K-functional, translation operator, best approximation, several variables
Applied Mathematics, Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable, Multidimensional problems, General harmonic expansions, frames, Modulus of smoothness, Approximation by other special function classes, \(K\)-functional, Computational Mathematics, Several variables, modulus of smoothness, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Best approximation, Translation operator, K-functional, translation operator, best approximation, several variables
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