Diagonalization of shift-preserving operators (Q2048609)
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scientific article; zbMATH DE number 7384211
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Diagonalization of shift-preserving operators |
scientific article; zbMATH DE number 7384211 |
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Diagonalization of shift-preserving operators (English)
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23 August 2021
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It is studied the structure of shift-preserving operators acting on a finitely generated shift-invariant space in this work. A new notion of diagonalization for these operators, which is called s-diagonalization is defined. Necessary and sufficient conditions on a bounded shift-preserving operator in order to be s-diagonalizable are given. These conditions are in terms of its range operator. A generalized Spectral Theorem for normal bounded shift-preserving operators is also obtained.
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shift-invariant spaces
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shift-preserving operators
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range function
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range operator
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diagonalization
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