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Multipliers on Spaces of Functions on a Locally Compact Abelian Group with Values in a Hilbert Space

Petkova, Violeta (2006)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary 43A22, 43A25.We prove a representation theorem for bounded operators commuting with translations on L2ω(G,H), where G is a locally compact abelian group, H is a Hilbert space and ω is a weight on G. Moreover, in the particular case when G = R, we characterize completely the spectrum of the shift operator S1,ω on Lω2(R,H).

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