We consider compact selfadjoint pseudodifferential operators under the assumption that the decay order of symbols with respect to ξ depends on a point x. We show that the asymptotic Weyl formula is valid for such operators. Bibliography: 12 titles.
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Dedicated with thanks to Nina Nikolaevna Uraltseva
Translated from Problemy Matematicheskogo Analiza 78, January 2015, pp. 111-121.
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Karol’, A.I. Asymptotic Behavior of the Spectrum of Pseudodifferential Operators of Variable Order. J Math Sci 207, 236–248 (2015). https://doi.org/10.1007/s10958-015-2369-6
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DOI: https://doi.org/10.1007/s10958-015-2369-6