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- W3159743923 abstract "In this paper, we prove the existence of a particular diagonalization for normal bounded operators defined on subspaces of $$L^2({mathfrak {S}})$$ where $${mathfrak {S}}$$ is a second countable LCA group. The subspaces where the operators act are invariant under the action of a group $$Gamma $$ which is a semi-direct product of a uniform lattice of $${mathfrak {S}}$$ with a discrete group of automorphisms. This class includes the crystal groups which are important in applications as models for images. The operators are assumed to be $$Gamma $$ preserving. i.e. they commute with the action of $$Gamma $$ . In particular we obtain a spectral decomposition for these operators. This generalizes recent results on shift-preserving operators acting on lattice invariant subspaces where $${mathfrak {S}}$$ is the Euclidean space." @default.
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- W3159743923 date "2021-04-27" @default.
- W3159743923 modified "2023-10-18" @default.
- W3159743923 title "The structure of group preserving operators" @default.
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- W3159743923 doi "https://doi.org/10.1007/s43670-021-00005-3" @default.
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