About spaces of $\omega_1$-$\omega_2$-ultradifferentiable functions
Copyright policy )About spaces of $\omega_1$-$\omega_2$-ultradifferentiable functions
Nonisotropic spaces of ultradifferentiable functions are introduced on products \( \Omega_1 \times \Omega_2 \subset \mathbb R^r \times \mathbb R^s \) in such a way that the first \(r\) partial derivatives are governed by a weight function \( \omega_1 \) in the sense of \textit{R.\,W.\thinspace Braun, R.\,Meise} and \textit{B.\,A.\thinspace Taylor} [Result.\ Math.\ 17, No.\,3--4, 206--237 (1990; Zbl 0735.46022)] and the other partial derivatives are governed by a possibly different weight \( \omega_2 \). In this setting, a theory is evolved, leading to kernel theorems. Proofs are only carried out if they differ from the proofs of the analogous theory for the Denjoy-Carleman case, which the same authors developed in [Result.\ Math.\ 53, No.\,1--2, 173--195 (2009; Zbl 1182.46025)].
Beurling type, kernel theorem, 46F05, Topological linear spaces of test functions, distributions and ultradistributions, tensor product, 46A32, 46A11, Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.), ultradifferentiable functions, Roumieu type, Spaces of linear operators; topological tensor products; approximation properties, Roumieu class, Topological linear spaces of continuous, differentiable or analytic functions, nuclearity, 46E10, Beurling class
Beurling type, kernel theorem, 46F05, Topological linear spaces of test functions, distributions and ultradistributions, tensor product, 46A32, 46A11, Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.), ultradifferentiable functions, Roumieu type, Spaces of linear operators; topological tensor products; approximation properties, Roumieu class, Topological linear spaces of continuous, differentiable or analytic functions, nuclearity, 46E10, Beurling class
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