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Images of some functions and functional spaces under the Dunkl-Hermite semigroup

Néjib Ben Salem, Walid Nefzi (2013)

Commentationes Mathematicae Universitatis Carolinae

We propose the study of some questions related to the Dunkl-Hermite semigroup. Essentially, we characterize the images of the Dunkl-Hermite-Sobolev space, 𝒮 ( ) and L α p ( ) , 1 < p < , under the Dunkl-Hermite semigroup. Also, we consider the image of the space of tempered distributions and we give Paley-Wiener type theorems for the transforms given by the Dunkl-Hermite semigroup.

Inverses of generators of nonanalytic semigroups

Ralph deLaubenfels (2009)

Studia Mathematica

Suppose A is an injective linear operator on a Banach space that generates a uniformly bounded strongly continuous semigroup e t A t 0 . It is shown that A - 1 generates an O ( 1 + τ ) A ( 1 - A ) - 1 -regularized semigroup. Several equivalences for A - 1 generating a strongly continuous semigroup are given. These are used to generate sufficient conditions on the growth of e t A t 0 , on subspaces, for A - 1 generating a strongly continuous semigroup, and to show that the inverse of -d/dx on the closure of its image in L¹([0,∞)) does not generate a strongly...

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