The spectra of random pseudo-differential operators

Jingbo Xia

doi:10.1090/S0002-9947-1994-1250828-5

The spectra of random pseudo-differential operators

Jingbo Xia

Mathematics

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Abstract

We study the spectra of random pseudo-differential operators generated by the same symbol function on different L2 -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.

Original language	English
Pages (from-to)	381-411
Number of pages	31
Journal	Transactions of the American Mathematical Society
Volume	345
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9947-1994-1250828-5
State	Published - Sep 1994

Keywords

Dynamical system
Pseudo-differential operator
Spectrum

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10.1090/S0002-9947-1994-1250828-5

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AB - We study the spectra of random pseudo-differential operators generated by the same symbol function on different L2 -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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KW - Pseudo-differential operator

KW - Spectrum

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The spectra of random pseudo-differential operators

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Keywords

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