KERNEL THEOREMS FOR OPERATORS ON CO-ORBIT SPACES ASSOCIATED WITH LOCALISED FRAMES - Université de Lorraine Access content directly
Preprints, Working Papers, ... Year : 2024

KERNEL THEOREMS FOR OPERATORS ON CO-ORBIT SPACES ASSOCIATED WITH LOCALISED FRAMES

Abstract

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.
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hal-04484413 , version 1 (29-02-2024)

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Dimitri Bytchenkoff, Michael Speckbacher, Peter Balazs. KERNEL THEOREMS FOR OPERATORS ON CO-ORBIT SPACES ASSOCIATED WITH LOCALISED FRAMES. 2024. ⟨hal-04484413⟩
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