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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The absolute continuity of phase operators


Authors: J. Dombrowski and G. H. Fricke
Journal: Trans. Amer. Math. Soc. 213 (1975), 363-372
MSC: Primary 47B15
MathSciNet review: 0377573
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Abstract: This paper studies the spectral properties of a class of operators known as phase operators which originated in the study of harmonic oscillator phase. Ifantis conjectured that such operators had no point spectrum. It was later shown that certain phase operators were, in fact, absolutely continuous and that all phase operators at least had an absolutely continuous part. The present work completes the discussion by showing that all phase operators are absolutely continuous.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1975-0377573-0
PII: S 0002-9947(1975)0377573-0
Keywords: Phase operators, absolute continuity of phase operators, real parts of weighted shifts
Article copyright: © Copyright 1975 American Mathematical Society