Kernel theorems for operators on co-orbit spaces associated with localised frames
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910453478719488 |
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| author | Bytchenkoff, Dimitri Speckbacher, Michael Balazs, Peter |
| author_facet | Bytchenkoff, Dimitri Speckbacher, Michael Balazs, Peter |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18367 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kernel theorems for operators on co-orbit spaces associated with localised frames Bytchenkoff, Dimitri Speckbacher, Michael Balazs, Peter Functional Analysis 42B35, 42C15, 46A32, 47B34 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. |
| title | Kernel theorems for operators on co-orbit spaces associated with localised frames |
| topic | Functional Analysis 42B35, 42C15, 46A32, 47B34 |
| url | https://arxiv.org/abs/2402.18367 |