Ideal-triangularizability of upward directed sets of positive operators.
We propose the study of some questions related to the Dunkl-Hermite semigroup. Essentially, we characterize the images of the Dunkl-Hermite-Sobolev space, and , , 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.
Suppose A is an injective linear operator on a Banach space that generates a uniformly bounded strongly continuous semigroup . It is shown that generates an -regularized semigroup. Several equivalences for generating a strongly continuous semigroup are given. These are used to generate sufficient conditions on the growth of , on subspaces, for 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...