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

1
Department of Mathematics, Federal University of Paraná, Curitiba 81531-980, Brazil
2
Department of Mathematics, University of Turin, Via Carlo Alberto 10, 10123 Turin, Italy
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(11), 1938; https://doi.org/10.3390/math8111938
Received: 29 September 2020 / Revised: 28 October 2020 / Accepted: 29 October 2020 / Published: 3 November 2020
(This article belongs to the Special Issue Microlocal and Time-Frequency Analysis)
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. View Full-Text
Keywords: pseudodifferential operators; Gevrey regularity; sharp Gårding inequality; p-evolution equations pseudodifferential operators; Gevrey regularity; sharp Gårding inequality; p-evolution equations
MDPI and ACS Style

Arias Junior, A.; Cappiello, M. On the Sharp Gårding Inequality for Operators with Polynomially Bounded and Gevrey Regular Symbols. Mathematics 2020, 8, 1938. https://doi.org/10.3390/math8111938

AMA Style

Arias Junior A, Cappiello M. On the Sharp Gårding Inequality for Operators with Polynomially Bounded and Gevrey Regular Symbols. Mathematics. 2020; 8(11):1938. https://doi.org/10.3390/math8111938

Chicago/Turabian Style

Arias Junior, Alexandre, and Marco Cappiello. 2020. "On the Sharp Gårding Inequality for Operators with Polynomially Bounded and Gevrey Regular Symbols" Mathematics 8, no. 11: 1938. https://doi.org/10.3390/math8111938

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