Representation and approximation of multivariate functions with mixed smoothness by hyperbolic wavelets

In this paper, we study the representation theorems of multivariate functions with mixed smoothness by wavelet basis formed by tensor products of univariate wavelets, we also study the best approximation in the L q( R d) metric for some function classes with mixed smoothness by hyperbolic wavelets a...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 291; no. 2; pp. 698 - 715
Main Author: Heping, Wang
Format: Journal Article
Language:English
Published: San Diego, CA Elsevier Inc 15.03.2004
Elsevier
Subjects:
Approximations and expansions
Best approximation
Decomposition of functions
Exact sciences and technology
Functions with mixed smoothness
Hyperbolic wavelets
Mathematical analysis
Mathematics
Sciences and techniques of general use
Special functions
Best approximation
Decomposition of functions
Hyperbolic wavelets
Functions with mixed smoothness
Numerical approximation
Wavelets
Mathematical analysis
Tensor product
N variable function
Asymptotic approximation
Function approximation
Function representation
ISSN:0022-247X, 1096-0813
Online Access:Get full text
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Summary:In this paper, we study the representation theorems of multivariate functions with mixed smoothness by wavelet basis formed by tensor products of univariate wavelets, we also study the best approximation in the L q( R d) metric for some function classes with mixed smoothness by hyperbolic wavelets and obtain some asymptotic estimates of approximating order.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2003.11.023