46 research outputs found
Solution to the first Cousin problem for vector-valued quasianalytic functions
We study spaces of vector-valued quasianalytic functions and solve the first
Cousin problem in these spaces.Comment: 23 page
A projective description of generalized Gelfand-Shilov spaces of Roumieu type
We provide a projective description for a class of generalized Gelfand-Shilov
spaces of Roumieu type. In particular, our results apply to the classical
Gelfand-Shilov spaces and weighted -spaces of ultradifferentiable
functions of Roumieu type.Comment: 10 page
Discrete characterizations of wave front sets of Fourier-Lebesgue and quasianalytic type
We obtain discrete characterizations of wave front sets of Fourier-Lebesgue
and quasianalytic type. It is shown that the microlocal properties of an
ultradistribution can be obtained by sampling the Fourier transforms of its
localizations over a lattice in . In particular, we prove the
following discrete characterization of the analytic wave front set of a
distribution . Let be a lattice in
and let be an open convex neighborhood of the origin such
that . The analytic wave front set
coincides with the complement in
of the set of points for which there are an open neighborhood
of , an open conic neighborhood of
, and a bounded sequence in
with on such that for some Comment: 21 page