Full paper in PDF:
$%S. N. Melikhov, Generalized fourier expansions for distributions and ultradistributions,
Rev. Mat. Complut. 12 (1999), no. 2, 349–379.%$
ABSTRACT
Let
be a space of distributions or ultradistributions of Beurling
type on the
-dimensional parallelepiped
. We
investigate the following problems: 1) When can any element of
be
expanded in absolutely convergent series in a system of generalized exponentials
with special exponents
,
. 2) When can a sequence
of the coefficients
in an expansion
be chosen
so that it depends in a continuous and linear way on
, where
for all
.
1991 Mathematics Subject Classification: 46F05,42C15.