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arXiv:2210.16793 (math)
[Submitted on 30 Oct 2022 (v1), last revised 21 Jun 2023 (this version, v2)]

Title:Approximation on hexagonal domains by Taylor-Abel-Poisson means

Authors:Jürgen Prestin, Viktor Savchuk, Andrii Shidlich
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Abstract:Approximative properties of the Taylor-Abel-Poisson linear summation me\-thod of Fourier series are considered for functions of several variables, periodic with respect to the hexagonal domain, in the integral metric. In particular, direct and inverse theorems are proved in terms of approximations of functions by the Taylor-Abel-Poisson means and $K$-functionals generated by radial derivatives. Bernstein type inequalities for $L_1$-norm of high-order radial derivatives of the Poisson kernel are also obtained.
Comments: arXiv admin note: text overlap with arXiv:1609.09615, arXiv:1901.06275
Subjects: Classical Analysis and ODEs (math.CA); Numerical Analysis (math.NA)
MSC classes: 41A27, 42A16, 41A44
Cite as: arXiv:2210.16793 [math.CA]
  (or arXiv:2210.16793v2 [math.CA] for this version)
  https://doi.org/10.48550/arXiv.2210.16793
Related DOI: https://doi.org/10.1016/j.jmaa.2023.127536

Submission history

From: Andrii Shidlich L. [view email]
[v1] Sun, 30 Oct 2022 09:43:08 UTC (16 KB)
[v2] Wed, 21 Jun 2023 04:32:36 UTC (18 KB)
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