Geodesic
Harmonic analysis of causal operators and their spectral properties
Izvestiya. Mathematics , Tome 69 (2005) no. 3, pp. 439-486

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The definition and study of causal operators are based on the representation theory of group algebras. We study the structure of the spectra of causal operators, obtain conditions for causal invertibility and state criteria for a causal operator to belong to the radical. 
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     author = {A. G. Baskakov and I. A. Krishtal},
     title = {Harmonic analysis of causal operators and their spectral properties},
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A. G. Baskakov; I. A. Krishtal. Harmonic analysis of causal operators and their spectral properties. Izvestiya. Mathematics , Tome 69 (2005) no. 3, pp. 439-486. http://geodesic.mathdoc.fr/item/IM2_2005_69_3_a0/