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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On some spectral properties of elliptic pseudodifferential operators


Author: M. W. Wong
Journal: Proc. Amer. Math. Soc. 99 (1987), 683-689
MSC: Primary 47G05; Secondary 35S05
MathSciNet review: 877040
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0877040-5
PII: S 0002-9939(1987)0877040-5
Keywords: Elliptic pseudodifferential operators, minimal operators, maximal operators, relative compactness
Article copyright: © Copyright 1987 American Mathematical Society