On convergence rates in approximation theory for operator semigroups

2013/07/05 by A. M. Gomilko, Yuri Tomilov, Gomilko, Alexander +1
Computer Science · Mathematics · #47D03 #65J08 #65M12 #Advanced Banach Space Theory #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Primary: 47A60 #Secondary: 46N40

paper · pdf · doi:10.48550/arxiv.1307.1626

openalex publication_date 2013/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We create a new, functional calculus, approach to approximation of C₀-semigroups on Banach spaces. As an application of this approach, we obtain optimal convergence rates in classical approximation formulas for C₀-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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