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Erschienen in:
2012 | OriginalPaper | Buchkapitel
Subordination
verfasst von : Jan Prüss
Erschienen in: Evolutionary Integral Equations and Applications
Verlag: Springer Basel
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The class of completely positive kernels plays a prominent role in the theory of vector-valued Volterra equations, and appears in applications quite naturally. This class of kernels, its properties and associated creep functions are discussed thoroughly in this section. By means of the principle of subordination it is possible to construct new resolvents from a given one, e.g. from a
C
0-semigroup or from a cosine family. The new resolvent can be explicitly represented in terms of the given one, and of the propagation function associated with a completely positive kernel. This representation is particularly useful for the understanding of the regularity and the asymptotic behaviour of the resolvent.