Let S be a dense sub-semigroup of R+, and let X be a separable, reflexive Banach space. This note contains a proof that every weakly continuous contractive semigroup of operators on X over S can be extended to a weakly continuous semigroup over R+. We obtain similar results for nonlinear, nonexpansive semigroups as well. As a corollary we characterize all densely parametrized semigroups which a...

We consider continuous semigroups of analytic functions {Φt}t≥0 in the so-called Gordon-Hedenmalm class G, that is, family Φ:C+→C+ giving rise to bounded composition operators Hardy space Dirichlet series H2. show there is a one-to-one correspondence between G and strongly {Tt}t≥0, where Tt(f)=f∘Φt, f∈H2. extend these results for range p∈[1,∞). For case p=∞, we prove no non-trivial semigroup H∞...

In this paper, we present new existence theorems of mild solutions to Cauchy problem for some fractional differential equations with delay. Our main tools to obtain our results are the theory of analytic semigroups and compact semigroups, the Kuratowski measure of non-compactness, and fixed point theorems, with the help of some estimations. Examples are also given to illustrate the applicabilit...

Let S be a dense sub-semigroup of R+, and let X be a separable, reflexive Banach space. This note contains a proof that every weakly continuous contractive semigroup of operators on X over S can be extended to a weakly continuous semigroup over R+. We obtain similar results for nonlinear, non-expansive semigroups as well. As a corollary we characterize all densely parametrized semigroups which ...