A general approach to approximation theory of operator semigroups

Autor:	Gomilko, A., Kosowicz, S., Tomilov, Yu.
Rok vydání:	2018
Předmět:	Mathematics - Functional Analysis Mathematics - Analysis of PDEs Mathematics - Numerical Analysis
Druh dokumentu:	Working Paper
Popis:	We develop a general, functional calculus approach to approximation of $C_0$-semigroups on Banach spaces by bounded completely monotone functions of their generators. The approach comprises most of well-known approximation formulas, yields optimal convergence rates, and sometimes even leads to sharp constants. In an important particular case when semigroups are holomorphic, we are able to significantly improve our results for general semigroups. Moreover, we present several second order approximation formulas with rates, which in such a general form appear in the literature for the first time. Comment: 53 pages, This is a version of the paper to appear in Journal de Math\'ematiques Pures et Appliqu\'ees
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1801.06749 Zobrazit plný text záznamu View this record from Arxiv