Premium
On the Asymptotic Behavior of Perturbed Strongly Continuous Semigroups
Author(s) -
Brendle Simon
Publication year - 2001
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200106)226:1<35::aid-mana35>3.0.co;2-r
Subject(s) - mathematics , semigroup , banach space , compact space , exponential stability , bounded function , norm (philosophy) , pure mathematics , generator (circuit theory) , perturbation (astronomy) , mathematical analysis , law , nonlinear system , power (physics) , physics , quantum mechanics , political science
For a strongly continuous semigroup ( T ( t )) t ≥0 with generator A on a Banach space X and an A –bounded perturbation B we characterize norm continuity and compactness of the terms in the Dyson–Phillips series of the perturbed semigroup ( S ( t )) t ≥0 .This allows us to characterize uniform exponential stability of ( S ( t )) t ≥0 by spectral conditions on ( T ( t )) t ≥0 and A + B. The results are applied to a delay differential equation.