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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 spectra of random pseudo-differential operators


Author: Jingbo Xia
Journal: Trans. Amer. Math. Soc. 345 (1994), 381-411
MSC: Primary 47G30; Secondary 35R60, 35S99, 46L99
MathSciNet review: 1250828
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Abstract: We study the spectra of random pseudo-differential operators generated by the same symbol function on different $ {L^2}$-spaces. Our results generalize the spectral coincidence theorem of S. Kozlov and M. Shubin (Math. USSRSb. 51 (1985), 455-471) for elliptic operators of positive order associated with ergodic systems. Because of our new approach, we are able to treat operators of arbitrary order and associated with arbitrary dynamical systems. Furthermore, we characterize the spectra of these operators in terms of certain naturally obtained Borel measures on R.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1250828-5
PII: S 0002-9947(1994)1250828-5
Keywords: Pseudo-differential operator, spectrum, dynamical system
Article copyright: © Copyright 1994 American Mathematical Society