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arXiv · 2111.07469

Analytic functional calculus and Gårding inequality on graded Lie groups with applications to diffusion equations

Duván Cardona·Julio Delgado·Michael Ruzhansky
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Abstract

In this paper we study the Cauchy problem for diffusion equations associated to a class of strongly hypoelliptic pseudo-differential operators on graded Lie groups. To do so, we develop a global complex functional calculus on graded Lie groups in order to analyse the corresponding energy estimates. One of the main aspects of this complex functional calculus is that for the $(ρ,δ)$-Euclidean Hörmander classes we recover the standard functional calculus developed by Seeley [38]. In consequence the Gårding inequality that we prove for arbitrary graded Lie groups absorbs the historical 1953's inequality due to Gårding [26].

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Duván Cardona, Julio Delgado, Michael Ruzhansky. 2021-11-14. Analytic functional calculus and Gårding inequality on graded Lie groups with applications to diffusion equations. https://arxiv.org/abs/2111.07469

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