Convoluted C-operator families and abstract Cauchy problems
Marko Kostić, Stevan Pilipović (2007)
Kragujevac Journal of Mathematics
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Displaying similar documents to “Perturbation theorems for convoluted -semigroups and cosine functions”
Convoluted C-operator families and abstract Cauchy problems
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This paper is concerned with α-times integrated C-semigroups for α > 0 and the associated abstract Cauchy problem: , t >0; u(0) = 0. We first investigate basic properties of an α-times integrated C-semigroup which may not be exponentially bounded. We then characterize the generator A of an exponentially bounded α-times integrated C-semigroup, either in terms of its Laplace transforms or in terms of existence of a unique solution of the above abstract Cauchy problem for every x...
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