Abstract
We derive the complete asymptotic expansion for the quasiinterpolants of Gauss Weierstrass operators \(W_{n}\) and their left quasi interpolants \(W_{n}^{[r]}\) with explicit representation of the coefficients. The results apply to all locally integrable real functions \(f\) on \(\mathbb{R}\) satisfying the growth condition \(f(t)=O\left(e^{ct^{2}}\right)\ \)as \(\ |t|\rightarrow+\infty\), for some \(c>0\). All expansions are shown to be valid also for simultaneous approximation.
Authors
U. Abel
Octavian Agratini
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
R. Păltănea
Keywords
Approximation by integral operators, rate of convergence, degree of approximation, asymptotic expansions.
Paper coordinates
U. Abel, O. Agratini, R. Păltănea, A complete asymptotic expansion for the quasi-interpolants of Gauss–Weierstrass operators, Mediterranean Journal of Mathematics 15 (2018), pp. 154-156, https://doi.org/10.1007/s00009-018-1195-8
requires subscription: https://doi.org/10.1007/s00009-018-1195-8
About this paper
Journal
Mediteranean Journal of Mathematics
Publisher Name
Springer
Print ISSN
Online ISSN
1660-5454
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