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Spectral analysis of unitary band matrices. (English) Zbl 1029.47016

Summary: This paper is devoted to the spectral properties of a class of unitary operators with a matrix representation displaying a band structure. Such band matrices appear as monodromy operators in the study of certain quantum dynamical systems. These doubly infinite matrices essentially depend on an infinite sequence of phases which govern their spectral properties. We prove the spectrum to be purely singular for random phases and purely absolutely continuous in case they provide the doubly infinite matrix with a periodic structure in the diagonal direction. We also study some properties of the singular spectrum of such matrices considered as infinite in one direction only.

MSC:

47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
47A10 Spectrum, resolvent
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
47N50 Applications of operator theory in the physical sciences
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