On hyperbolic summation and hyperbolic moduli of smoothness
type: Item
instance of: scholarly article
title: On hyperbolic summation and hyperbolic moduli of smoothness
zbMATH Open document ID: 0857.41007
DOI: 10.1007/BF02432857
published in: Constructive Approximation
publication date: 1996-09-12T00:00:00Z
review text: For the functions of one variable, the relation between smoothness of a function and the order of the best approximation by trigonometric polynomials or spline functions with given knots is well understood. The situation is different in the multidimensional case of tensor products, as we have several possible orders. This paper deals with the method of hyperbolic summation of tensor product orthogonal spline functions on \([0,1]^d\). The spaces, defined in terms of the order of the best approximation by the elements of the space spanned by the tensor product functions with indices from a given hyperbolic set, are described both in terms of the coefficients in some basis and as interpolation spaces. Moreover, the hyperbolic modulus of smoothness is studied, and some relations between hyperbolic summation and hyperbolic modulus of smoothness are established.
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 895634
zbMATH Keywords: orthonormal spline
zbMATH Keywords: hyperbolic modulus of smoothness
zbMATH Keywords: hyperbolic summation
author: Anna Kamont
reviewed by: H. P. Dikshit
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 895634