On the characterization of Gelfand-Shilov-Roumieu spaces

الأصل · EN

Generalized m-Gelfand-Shilov-Roumieu vector spaces Sₘ(X) are introduced. Here m = (m⁽¹⁾,...,m⁽ⁿ⁾), X=(X₁,...,Xₙ) and m⁽¹⁾,...,m⁽ⁿ⁾ are sequences of positive real numbers and X₁,...,Xₙ are operators in a Hilbert space. Conditions are given on the sequences m⁽¹⁾,...,m⁽ⁿ⁾ and on the operators X₁,...,Xₙ so that the equality Sₘ(X) = Sₘ⁽¹⁾(X₁)∩... ∩Sₘ⁽ⁿ⁾(Xₙ) is valid. As a corollary we obtain a new proof of a characterization theorem for classical Gelfand-Shilov spaces.