On some spectral properties of elliptic pseudodifferential operators

Wong, M. W.

doi:10.1090/S0002-9939-1987-0877040-5

On some spectral properties of elliptic pseudodifferential operators
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Proc. Amer. Math. Soc. 99 (1987), 683-689 Request permission

Abstract:

We prove that the minimal and maximal operators associated with an elliptic pseudodifferential operator coincide in ${L^p}({{\mathbf {R}}^n}),1 < p < \infty$. We obtain a set of necessary and sufficient conditions for a measurable function $q$ on ${{\mathbf {R}}^n}$ to be compact relative to some integral power of a constant coefficient elliptic pseudodifferential operator.

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