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Asymptotic Behavior of the Spectrum of Pseudodifferential Operators of Variable Order

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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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References

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  1. St. Petersburg State University, 28, Universitetskii pr., Petrodvorets, St. Petersburg, 198504, Russia

    A. I. Karol’

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  1. A. I. Karol’
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Correspondence to A. I. Karol’.

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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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