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- W4287996471 abstract "In this paper we study the properties of multiplication invariant (MI) operators acting on subspaces of the vector-valued space $L^2(X;mathcal H)$. We characterize such operators in terms of range functions by showing that there is an isomorphism between the category of MI spaces (with MI operators as morphisms) and the category of measurable range functions whose morphisms are measurable range operators. We investigate how global properties of an MI operator are reflected by local pointwise properties of its corresponding range operator. We also establish several results about frames generated by multiplications in $L^2(X;mathcal H)$. This includes the classification of frames of multiplications with respect to unitary equivalence by measurable fields of Gramians. Finally, we show applications of our results in the study of abelian group frames and translation-invariant (TI) operators acting on subspaces of $L^2(mathcal G)$, where $mathcal G$ is a locally compact group." @default.
- W4287996471 created "2022-07-26" @default.
- W4287996471 creator A5002853431 @default.
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- W4287996471 date "2019-12-09" @default.
- W4287996471 modified "2023-09-24" @default.
- W4287996471 title "Multiplication-invariant operators and the classification of LCA group frames" @default.
- W4287996471 doi "https://doi.org/10.48550/arxiv.1912.04420" @default.
- W4287996471 hasPublicationYear "2019" @default.
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