KERNEL THEOREMS FOR OPERATORS ON CO-ORBIT SPACES ASSOCIATED WITH LOCALISED FRAMES
Résumé
Kernel theorems, in general, provide a convenient representation of bounded linear operators. For the operator acting on a concrete function space, this means that its action on any element of the space can be expressed as a generalised integral operator, in a way reminiscent of the matrix representation of linear operators acting on finite dimensional vector spaces. We prove kernel theorems for bounded linear operators acting on co-orbit spaces associated with localised frames. Our two main results consist in characterising the spaces of operators whose generalised integral kernels belong to the co-orbit spaces of test functions and distributions associated with the tensor product of the localised frames respectively. Moreover, using a version of Schur's test, we establish a characterisation of the bounded linear operators between some specific co-orbit spaces.
Mots clés
Functional Analysis (math.FA)
FOS: Mathematics
42B35
42C15
46A32
47B34
2020 Mathematics subject classification: 42B35 42C15 46A32 47B34 Kernel theorem localised frames co-orbit spaces operator representation tensor products
2020 Mathematics subject classification: 42B35
47B34 Kernel theorem
localised frames
co-orbit spaces
operator representation
tensor products
Domaines
Mathématiques [math]Origine | Fichiers produits par l'(les) auteur(s) |
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Licence |