Operator norms of Gauss-Weierstrass operators and their left quasi interpolants
DOI:
https://doi.org/10.24193/subbmath.2019.2.08Keywords:
Approximation by positive operators, operator normAbstract
The paper deals with the Gau\ss --Weierstra\ss\ operators $W_{n}$and their left quasi interpolants $W_{n}^{\left[ r\right] }$. The quasi interpolants were defined by Paul Sablonni\`{e}re in 2014. Recently, their asymptotic behaviour was studied by Octavian Agratini, Radu P\u{a}lt\u{a}nea and the author by presenting complete asymptotic expansions. In this paper we derive
estimates for the operator norms of $W_{n}$ and $W_{n}^{\left[ r\right] }$ when acting on various function spaces.
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