Sparse grid approximation in weighted Wiener spaces

Sparse grid approximation in weighted Wiener spaces

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

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Veröffentlicht in:arXiv.org 2021-11
Hauptverfasser: Kolomoitsev, Yurii, Lomako, Tetiana, Tikhonov, Segey
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Approximation
Interpolation
Mathematical analysis
Norms
Operators
Periodic functions
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Tikhonov, Segey
description We study approximation properties of multivariate periodic functions from weighted Wiener spaces by sparse grids 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 grids methods in weighted Wiener norms as well as analogues of the Littlewood-Paley-type characterizations in terms of families of quasi-interpolation operators.
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Norms
Operators
Periodic functions
title Sparse grid approximation in weighted Wiener spaces
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