Journalartikel
Autorenliste: Berdysheva, Elena E.; Dyn, Nira; Farkhi, Elza; Mokhov, Alona
Jahr der Veröffentlichung: 2021
Zeitschrift: Journal of Fourier Analysis and Applications
Bandnummer: 27
Heftnummer: 2
ISSN: 1069-5869
eISSN: 1531-5851
Open Access Status: Hybrid
DOI Link: https://doi.org/10.1007/s00041-021-09812-7
Verlag: Springer
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.
Zitierstile
Harvard-Zitierstil: Berdysheva, E., Dyn, N., Farkhi, E. and Mokhov, A. (2021) Metric Fourier Approximation of Set-Valued Functions of Bounded Variation, Journal of Fourier Analysis and Applications, 27(2), Article 17. https://doi.org/10.1007/s00041-021-09812-7
APA-Zitierstil: Berdysheva, E., Dyn, N., Farkhi, E., & Mokhov, A. (2021). Metric Fourier Approximation of Set-Valued Functions of Bounded Variation. Journal of Fourier Analysis and Applications. 27(2), Article 17. https://doi.org/10.1007/s00041-021-09812-7
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