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arXiv · 1701.07907

Spectral asymptotics for infinite order pseudo-differential operators

Stevan Pilipović·Bojan Prangoski·Jasson Vindas
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Abstract

We study spectral properties of a class of global infinite order pseudo-differential operators and obtain the asymptotic behaviour of the spectral counting functions of such operators. Unlike their finite order counterparts, their spectral asymptotics are not of power-log-type but of log-type. The ultradistributional setting of such operators of infinite order makes the theory more complex so that the standard finite order global Weyl calculus cannot be used in this context.

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Stevan Pilipović, Bojan Prangoski, Jasson Vindas. 2018-02-18. Spectral asymptotics for infinite order pseudo-differential operators. https://doi.org/10.1007/s13373-017-0114-9

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