Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/4097

 Title: Metric Fourier Approximation of Set-Valued Functions of Bounded Variation Authors: Berdysheva, Elena E.Dyn, NiraFarkhi, ElzaMokhov, Alona Keywords: Compact SetsSet-valued FunctionsFunction of Bounded VariationMetric SelectionsMetric Linear CombinationsMetric IntegralMetric approximation OperatorsTrigonometric Fourier Approximation Issue Date: 11-Jan-2021 Publisher: Springer Citation: Berdysheva, E.E., Dyn, N., Farkhi, E. et al. Metric Fourier Approximation of Set-Valued Functions of Bounded Variation. J Fourier Anal Appl 27, 17 (2021). https://doi.org/10.1007/s00041-021-09812-7 Series/Report no.: J Fourier Anal Appl;27(17) Abstract: We introduce and investigate an adaptation of Fourier series to set-valued functions (multifunctions, SVFs) of bounded variation. In our approach we define an analogue of the partial sums of the Fourier series with the help of the Dirichlet kernel using the newly defined weighted metric integral. We derive error bounds for these approximants. As a consequence, we prove that the sequence of the partial sums converges pointwisely in the Hausdorff metric to the values of the approximated set-valued function at its points of continuity, or to a certain set described in terms of the metric selections of the approximated multifunction at a point of discontinuity. Our error bounds are obtained with the help of the new notions of one-sided local moduli and quasi-moduli of continuity which we discuss more generally for functions with values in metric spaces. URI: http://hdl.handle.net/10525/4097 ISSN: 1069-5869 Appears in Collections: Q1

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