On the characterization of Gelfand-Shilov-Roumieu spaces

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Abstract: Generalized

m a t h b f m

-Gelfand-Shilov-Roumieu vector spaces

m a t h c a l S_{m a t h b f m} (m a t h b f X)

are introduced. Here

m a t h b f m = (m^{(1)}, ..., m^{(n)})

,

m a t h b f X = (X_{1}, ..., X_{n})

and

m^{(1)}, ..., m^{(n)}

are sequences of positive real numbers and

X_{1}, ..., X_{n}

are operators in a Hilbert space. Conditions are given on the sequences

m^{(1)}, ..., m^{(n)}

and on the operators

X_{1}, ..., X_{n}

so that the equality

S_{m a t h b f m} (m a t h b f X) = S_{m^{(1)}} (X_{1}) c a p ... c a p S_{m^{(n)}} (X_{n})

is valid. As a corollary we obtain a new proof of a characterization theorem for classical Gelfand-Shilov spaces.

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