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2020 Semigroups on time scales and applications to abstract Cauchy problems
Hernán R. Henríquez, Carlos Lizama, Jaqueline G. Mesquita
Topol. Methods Nonlinear Anal. 56(1): 83-115 (2020). DOI: 10.12775/TMNA.2019.114

Abstract

In this paper, we introduce the definition of a $C_0$-semigroup on a time scale, which unifies the continuous, discrete and other cases which lie between them. Also, it extends the classical theory of operator semigroups to the quantum case. We study the relationship between the semigroup and its infinitesimal generator. We apply our theory to study the homogeneous and non homogeneous abstract Cauchy problem in Banach and Fréchet spaces.

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Hernán R. Henríquez. Carlos Lizama. Jaqueline G. Mesquita. "Semigroups on time scales and applications to abstract Cauchy problems." Topol. Methods Nonlinear Anal. 56 (1) 83 - 115, 2020. https://doi.org/10.12775/TMNA.2019.114

Information

Published: 2020
First available in Project Euclid: 11 June 2020

MathSciNet: MR4175072
Digital Object Identifier: 10.12775/TMNA.2019.114

Rights: Copyright © 2020 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.56 • No. 1 • 2020
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