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arXiv · 1909.03662

Polar decomposition of semigroups generated by non-selfadjoint quadratic differential operators and regularizing effects

Paul Alphonse·Joackim Bernier
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Abstract

We characterize geometrically the regularizing effects of the semigroups generated by accretive non-selfadjoint quadratic differential operators. As a byproduct, we establish the subelliptic estimates enjoyed by these operators, being expected to be optimal. These results prove conjectures by M. Hitrik, K. Pravda-Starov and J. Viola. The proof relies on a new representation of the polar decomposition of these semigroups. In particular, we identify the selfadjoint part as the evolution operator generated by the Weyl quantization of a time-dependent real-valued nonnegative quadratic form for which we prove a sharp anisotropic lower bound.

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Paul Alphonse, Joackim Bernier. 2019-09-09. Polar decomposition of semigroups generated by non-selfadjoint quadratic differential operators and regularizing effects. https://arxiv.org/abs/1909.03662

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