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Spectral analysis for convolution operators on locally compact groups

By M. Măntoiu and R. Tiedra De Aldecoa

Abstract

We consider operators Hµ of convolution with measures µ on locally compact groups. We characterize the spectrum of Hµ by constructing auxiliary operators whose kernel contain the pure point and singular subspaces of Hµ, respectively. The proofs rely on commutator methods. Key words and phrases: locally compact group, convolution operator, positive commutator, point spectrum, singular spectrum

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