Geodesic
Multipliers on Spaces of Functions on a Locally Compact Abelian Group with Values in a Hilbert Space
Serdica Mathematical Journal, Tome 32 (2006) no. 2-3, pp. 215-226.

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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).
Keywords: Multipliers, Translations, Spaces of Vector-Valued Functions 
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     author = {Petkova, Violeta},
     title = {Multipliers on {Spaces} of {Functions} on a {Locally} {Compact} {Abelian} {Group} with {Values} in a {Hilbert} {Space}},
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Petkova, Violeta. Multipliers on Spaces of Functions on a Locally Compact Abelian Group with Values in a Hilbert Space. Serdica Mathematical Journal, Tome 32 (2006) no. 2-3, pp. 215-226. http://geodesic.mathdoc.fr/item/SMJ2_2006_32_2-3_a5/