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1 Department of Mathematics Berkeley

Abstract : We study in this paper a notion of pseudo-spectrum in the semi-classical setting called injectivity pseudo-spectrum. The injectivity pseudo-spectrum is a subset of points in the complex plane where there exist some quasi-modes with a precise rate of decay. For that reason, these values can be considered as some `almost eigenvalues- in the semi-classical limit. We are interested here in studying the absence of injectivity pseudo-spectrum, which is characterized by a global a priori estimate. We prove in this paper a sharp global subelliptic a priori estimate for a class of pseudo-differential operators with respect to the regularity of their symbols. Our main result extends an a priori estimate of Dencker, Sjöstrand and Zworski for a class of pseudo-differential operators with symbols of limited smoothness violating the condition P.

Keywords : pseudospectrum subelliptic estimate limited smoothness





Author: Karel Pravda-Starov -

Source: https://hal.archives-ouvertes.fr/



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