Unbounded translation invariant operators on locally compact abelian groups (Q1900366)
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scientific article; zbMATH DE number 811182
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Unbounded translation invariant operators on locally compact abelian groups |
scientific article; zbMATH DE number 811182 |
Statements
Unbounded translation invariant operators on locally compact abelian groups (English)
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1 July 1996
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Let \(T : D(T) \subseteq L_p (G) \to L_p (G)\) be a densely defined linear operator. \(T\) is called translation invariant if and only if \(T\) is closable and commutes with translations. The author characterizes translation invariant operators on \(L_1 (G)\) and \(L_2 (G)\), where \(G\) is a locally compact abelian group. Also, he considers their relationship to translation invariant operators on \(L_p (G)\)-spaces.
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linear operator
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translation invariant
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locally compact abelian group
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