# A complete asymptotic expansion for the quasi-interpolants of Gauss–Weierstrass operators

## 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

## About this paper

##### Journal

Mediteranean Journal of Mathematics

Springer

1660-5446
##### Online ISSN

1660-5454

google scholar link

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