\(C_{0}\)-semigroups of linear operators on some ultrametric Banach spaces
type: Item
instance of: scholarly article
title: \(C_{0}\)-semigroups of linear operators on some ultrametric Banach spaces
zbMATH Open document ID: 1123.47054
DOI: 10.1155/IJMMS/2006/52398
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2007-06-13T00:00:00Z
full work available at URL: https://eudml.org/doc/53539
review text: The author describes non-Archimedean analogs of the basic notions of the theory of semigroups of linear operators on Banach spaces. The results given are quite easy and similar to the classical case, such as the generation of a semigroup by a bounded operator of a small norm, or a link from semigroups to abstract Cauchy problems. The converse link, which requires a uniqueness result, is not considered. For the nontrivial aspects of non-Archimedean abstract Cauchy problems, the reader may want to consult \textit{M. L. Gorbachuk} and \textit{V. I. Gorbachuk} [Methods Funct. Anal. Topol. 9, No. 3, 207--212 (2003; Zbl 1037.47052); Proceedings of the Steklov Institute of Mathematics 245, 91--97 (2004; Zbl 1105.34320)].
Mathematics Subject Classification ID: 47S10
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 34G10
zbMATH DE Number: 5164017
zbMATH Keywords: semigroup of operators
zbMATH Keywords: abstract Cauchy problem
zbMATH Keywords: ultrametric Banach space
author: Toka Diagana
reviewed by: Anatoly N. Kochubei
MaRDI profile type: Publication
cites work: Representations of the Weyl group in spaces of square integrable functions with respect top-adic valued Gaussian distributions
cites work: Q4659202
cites work: Towards a theory of some unbounded linear operators on \(p\)-adic Hilbert spaces and applications
cites work: An operator on some ultrametric Hilbert spaces
cites work: \(p\)-adic numbers: An introduction.
cites work: Q4841577
cites work: A Schrödinger-type equation over the field of p-adic numbers
cites work: p-adic commutation relations
cites work: Q4258887
cites work: Differential equations for \({\mathbb F}_q\)-linear functions
cites work: Pseudo-differential equations and stochastics over non-Archimedean fields
cites work: Q4702561
cites work: Semigroups of linear operators and applications to partial differential equations
cites work: An introduction to partial differential equations
cites work: Q4179411
cites work: Q4003475
description: scientific article; zbMATH DE number 5164017