Odd extension for fourier approximation of nonperiodic functions

Golovanov, R. V.; Калиткин, Н. Н.; Lutskiy, K. I.

doi:10.1134/s2070048213060069

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2014

2022

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Cited by 2 publications

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“…This article aims to extend the decay results obtained in [9] for univariate functions to two dimensions. The decay estimates for bivariate Fourier coefficients are obtained in [6] for a class of smooth functions. We derive decay estimates for bivariate Chebyshev coefficients of a large class of functions, including piecewise-smooth function with finite Vitali Variation.…”

Section: Introductionmentioning

confidence: 99%

Decay estimate of bivariate Chebyshev coefficients for functions with limited smoothness

Akansha¹

2022

Preprint

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We obtain the decay bounds for Chebyshev series coefficients of functions with finite Vitali variation on the unit square. A generalization of the well known identity, which relates exact and approximated coefficients, obtained using the quadrature formula, is derived. Finally, an asymptotic L 1 -approximation error of finite partial sum for functions of bounded variation in sense of Vitali as well as Hardy-Krause, on the unit square is deduced.

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Section: Introductionmentioning

confidence: 99%