On convergence rates in approximation theory for operator semigroups

Alexander Gomilko; Yuri Tomilov

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arXiv · 1307.1626

On convergence rates in approximation theory for operator semigroups

Alexander Gomilko·Yuri Tomilov

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Abstract

We create a new, functional calculus, approach to approximation of C_0-semigroups on Banach spaces. As an application of this approach, we obtain optimal convergence rates in classical approximation formulas for C_0-semigroups. In fact, our methods allow one to derive a number of similar formulas and equip them with sharp convergence rates. As a byproduct, we prove a new interpolation principle leading to efficient norm estimates in the Banach algebra of Laplace transforms of bounded measures on the semi-axis.

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BibTeX RIS

Alexander Gomilko, Yuri Tomilov. 2013-07-05. On convergence rates in approximation theory for operator semigroups. https://arxiv.org/abs/1307.1626

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