Translation-invariant linear forms on E′(G) and non-Liouville tuples on G

Asam, Lilian

doi:10.1016/0022-1236(88)90128-0

Journal of Functional Analysis

1988

DOI: 10.1016/0022-1236(88)90128-0

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Translation-invariant linear forms on E′(G) and non-Liouville tuples on G

Lilian Asam¹

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1989

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Linear operators commuting with translations on 𝒟(𝐑) are continuous

Meisters¹

1989

Proc. Amer. Math. Soc.

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Let D ( R ) \mathcal {D}\left ( {\mathbf {R}} \right ) denote the Schwartz space of all C ∞ {C^\infty } -functions f : R → C f:{\mathbf {R}} \to {\mathbf {C}} with compact supports in the real line R {\mathbf {R}} . An earlier result of the author on the automatic continuity of translation-invariant linear functionals on D ( R ) \mathcal {D}\left ( {\mathbf {R}} \right ) is combined with a general version of the Closed-Graph Theorem due to A. P. Robertson and W. J. Robertson in order to prove that every linear mapping S S of D ( R ) \mathcal {D}\left ( {\mathbf {R}} \right ) into itself, which commutes with translations, is automatically continuous.

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Linear operators commuting with translations on 𝒟(𝐑) are continuous

Meisters¹

1989

Proc. Amer. Math. Soc.

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Translation-invariant linear forms on E′(G) and non-Liouville tuples on G

Cited by 1 publication

References 17 publications

Linear operators commuting with translations on 𝒟(𝐑) are continuous

Linear operators commuting with translations on 𝒟(𝐑) are continuous

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