<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>C</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math>-semigroups of linear operators on some ultrametric Banach spaces

Diagana, Toka

doi:https://doi.org/10.1155/IJMMS/2006/52398

International Journal of Mathematics and Mathematical Sciences

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Volume 2006 | Article ID 052398 | https://doi.org/10.1155/IJMMS/2006/52398

C0-semigroups of linear operators on some ultrametric Banach spaces

Toka Diagana¹

Received20 Aug 2005

Revised28 Feb 2006

Accepted25 Apr 2006

Published26 Jun 2006

Abstract

C0-semigroups of linear operators play a crucial role in the solvability of evolution equations in the classical context. This paper is concerned with a brief conceptualization of C0-semigroups on (ultrametric) free Banach spaces E. In contrast with the classical setting, the parameter of a given C0-semigroup belongs to a clopen ball Ωr of the ground field K. As an illustration, we will discuss the solvability of some homogeneous p-adic differential equations.

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Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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