Geodesic
Multipliers on a Hilbert Space of Functions on R
Serdica Mathematical Journal, Tome 35 (2009) no. 2, pp. 207-216.

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For a Hilbert space H ⊂ L1loc(R) of functions on R we obtain a representation theorem for the multipliers M commuting with the shift operator S. This generalizes the classical result for multipliers in L2(R) as well as our previous result for multipliers in weighted space L2ω(R). Moreover, we obtain a description of the spectrum of S.
Keywords: Multipliers, Spectrum 
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Petkova, Violeta. Multipliers on a Hilbert Space of Functions on R. Serdica Mathematical Journal, Tome 35 (2009) no. 2, pp. 207-216. http://geodesic.mathdoc.fr/item/SMJ2_2009_35_2_a5/