The spectra of random pseudo-differential operators

Xia, Jingbo

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

The spectra of random pseudo-differential operators
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by Jingbo Xia

Trans. Amer. Math. Soc. 345 (1994), 381-411

DOI: https://doi.org/10.1090/S0002-9947-1994-1250828-5

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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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