On the Sharp Gårding Inequality for Operators with Polynomially Bounded and Gevrey Regular Symbols

Alexandre Arias Junior and Marco Cappiello
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Alexandre Arias Junior: Department of Mathematics, Federal University of Paraná, Curitiba 81531-980, Brazil
Marco Cappiello: Department of Mathematics, University of Turin, Via Carlo Alberto 10, 10123 Turin, Italy

Mathematics, 2020, vol. 8, issue 11, 1-23

Abstract: In this paper, we analyze the Friedrichs part of an operator with polynomially bounded symbol. Namely, we derive a precise expression of its asymptotic expansion. In the case of symbols satisfying Gevrey estimates, we also estimate precisely the regularity of the terms in the asymptotic expansion. These results allow new and refined applications of the sharp Gårding inequality in the study of the Cauchy problem for p -evolution equations.

Keywords: pseudodifferential operators; Gevrey regularity; sharp Gårding inequality; p -evolution equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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