C-semigroups and strongly continuous semigroups

1993 ◽  
Vol 81 (1-2) ◽  
pp. 227-255 ◽  
Author(s):  
Ralph deLaubenfels
Keyword(s):  
Strongly Continuous Semigroups

On the spectral mapping theorem for perturbed strongly continuous semigroups

2000 ◽  
Vol 74 (5) ◽  
pp. 365-378 ◽  
Author(s):  
S. Brendle ◽  
R. Nagel ◽  
J. Poland
Keyword(s):  
Spectral Mapping Theorem ◽  
Spectral Mapping ◽  
Strongly Continuous Semigroups

scholarly journals Non-power bounded generators of strongly continuous semigroups

2016 ◽  
Vol 436 (1) ◽  
pp. 429-438 ◽  
Author(s):  
Anna Golińska ◽  
Sven-Ake Wegner
Keyword(s):  
Strongly Continuous Semigroups ◽  
Power Bounded

scholarly journals Perturbation theory for dual semigroups II. Time-dependent perturbations in the sun-reflexive case

1988 ◽  
Vol 109 (1-2) ◽  
pp. 145-172 ◽  
Author(s):  
Ph. Clément ◽  
O. Diekmann ◽  
M. Gyllenberg ◽  
H. J. A. M. Heijmans ◽  
H. R. Thieme
Keyword(s):  
Banach Space ◽  
Functional Differential Equations ◽  
Time Dependent ◽  
Evolutionary System ◽  
Strongly Continuous Semigroups ◽  
Structured Population ◽  
Variation Of Constants ◽  
Retarded Functional Differential Equations ◽  
Functional Differential ◽  
Age Structured

SynopsisWe consider time-dependent perturbations of generators of strongly continuous semigroups on a Banach space. The perturbations map the Banach space into a bigger space, which is the second dual of the original space in a specific semigroup sense. Using the theory of dual semigroups we show that the solutions of a generalised variation-of-constants formuladefine an evolutionary system. We investigate continuity and differentiability propertiesof this evolutionary system and its dual system and examine in what sense the perturbed generator and its adjoint generate these evolutionary systems. It is shown that the results apply naturally to retarded functional differential equations and age structured population dynamics.

scholarly journals Strongly continuous semigroups on some Fréchet spaces

2014 ◽  
Vol 412 (1) ◽  
pp. 121-124 ◽  
Author(s):  
Leonhard Frerick ◽  
Enrique Jordá ◽  
Thomas Kalmes ◽  
Jochen Wengenroth
Keyword(s):  
Fréchet Spaces ◽  
Strongly Continuous Semigroups

A spectral mapping theorem for perturbed strongly continuous semigroups

1991 ◽  
Vol 291 (1) ◽  
pp. 453-462 ◽  
Author(s):  
F. Andreu ◽  
J. Mart�nez ◽  
J. M. Maz�n
Keyword(s):  
Spectral Mapping Theorem ◽  
Spectral Mapping ◽  
Strongly Continuous Semigroups
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