30 research outputs found
On a class of translation-invariant spaces of quasianalytic ultradistributions
A class of translation-invariant Banach spaces of quasianalytic
ultradistributions is introduced and studied. They are Banach modules over a
Beurling algebra. Based on this class of Banach spaces, we define corresponding
test function spaces and their strong duals
of quasianalytic type, and study convolution and
multiplicative products on . These new spaces
generalize previous works about translation-invariant spaces of tempered
(non-quasianalytic ultra-) distributions; in particular, our new considerations
apply to the settings of Fourier hyperfunctions and ultrahyperfunctions. New
weighted spaces of quasianalytic
ultradistributions are analyzed.Comment: 32 page
On quasianalytic classes of Gelfand-Shilov type. Parametrix and convolution
We develop a convolution theory for quasianalytic ultradistributions of
Gelfand-Shilov type. We also construct a special class of ultrapolynomials, and
use it as a base for the parametrix method in the study of new topological and
structural properties of several quasianalytic spaces of functions and
ultradistributions. In particular, our results apply to Fourier hyperfunctions
and Fourier ultra-hyperfunctions.Comment: 37 page