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.
Cite
@article{arxiv.2402.18367,
title = {Kernel theorems for operators on co-orbit spaces associated with localised frames},
author = {Dimitri Bytchenkoff and Michael Speckbacher and Peter Balazs},
journal= {arXiv preprint arXiv:2402.18367},
year = {2024}
}