Sparse Grid Approximation in Weighted Wiener Spaces

We study approximation properties of multivariate periodic functions from weighted Wiener spaces by sparse grid methods constructed with the help of quasi-interpolation operators. The class of such operators includes classical interpolation and sampling operators, Kantorovich-type operators, scaling...

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Bibliographic Details
Published in:The Journal of fourier analysis and applications 2023-04, Vol.29 (2), Article 19
Main Authors: Kolomoitsev, Yurii, Lomako, Tetiana, Tikhonov, Sergey
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Approximation
Approximations and Expansions
Fourier Analysis
Interpolation
Mathematical analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Norms
Operator Theory and Fourier Analysis
Operators
Partial Differential Equations
Periodic functions
Signal,Image and Speech Processing
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Summary:We study approximation properties of multivariate periodic functions from weighted Wiener spaces by sparse grid methods constructed with the help of quasi-interpolation operators. The class of such operators includes classical interpolation and sampling operators, Kantorovich-type operators, scaling expansions associated with wavelet constructions, and others. We obtain the rate of convergence of the corresponding sparse grid methods in weighted Wiener norms as well as analogues of the Littlewood–Paley-type characterizations in terms of families of quasi-interpolation operators.
ISSN:1069-5869
1531-5851
DOI:10.1007/s00041-023-09994-2