Journal of Operator Theory
Volume 72, Issue 2, Fall 2014 pp. 475-485.
On the characterization of Gelfand-Shilov-Roumieu
spaces
Authors:
Mihai Pascu
Author institution: Institute of Mathematics "Simion Stoilow"
of the Romanian Academy,
RO-014700 Bucharest, Romania, and "Petroleum-Gas" University of
Ploiesti, Bd. Bucuresti, 39, Ploiesti, Romania
Summary: Generalized $\mathbf{m}$-Gelfand--Shilov--Roumieu
vector spaces
$\mathcal{S}_{\mathbf{m}}(\mathbf{X})$\break are introduced.
Here $\mathbf{m}\!=\!(m^{(1)},\dots, m^{(n)})$, $\mathbf{X}\!=\!(X_{1},
\dots,
X_{n})$ and $m^{(1)},\dots, m^{(n)}$
are sequences of positive real numbers, while $X_{1},\dots,X_{n}$ are
operators in a Hilbert space.
Our definition extends ter Elst's definition of Gevrey vector spaces
\cite{TE2}.
Conditions are given on the sequences $m^{(1)},\dots,m^{(n)}$ and on the
operators
$X_{1},\dots,X_{n}$ so that the equality
${S}_{\mathbf{m}}(\mathbf{X})={S}_{m^{(1)}}(X_{1})\cap\dots
\cap{S}_{m^{(n)}}(X_{n})$ is valid. As a corollary we obtain a proof of a
characterization theorem for Gelfand-Shilov-Roumieu spaces.
DOI: http://dx.doi.org/10.7900/jot.2013jun04.2009
Keywords: Gelfand-Shilov-Roumieu vectors, Heisenberg group
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