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

Paul Alphonse 1 Joackim Bernier 2, 1
2 MINGUS - Multi-scale numerical geometric schemes
IRMAR - Institut de Recherche Mathématique de Rennes, ENS Rennes - École normale supérieure - Rennes, Inria Rennes – Bretagne Atlantique
Abstract : We study semigroups generated by accretive non-selfadjoint quadratic differential operators. We give a description of the polar decomposition of the associated evolution operators as products of a selfadjoint operator and a unitary operator. The selfadjoint parts turn out to be also evolution operators generated by time-dependent real-valued quadratic forms that are studied in details. As a byproduct of this decomposition, we give a geometric description of the regularizing properties of semigroups generated by accretive non-selfadjoint quadratic operators. Finally, by using the interpolation theory, we take advantage of this smoothing effect to establish subelliptic estimates enjoyed by quadratic operators.
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Pré-publication, Document de travail
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Soumis le : vendredi 6 septembre 2019 - 18:34:50
Dernière modification le : mercredi 11 septembre 2019 - 01:20:52

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  • HAL Id : hal-02280971, version 1
  • ARXIV : 1909.03662

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Paul Alphonse, Joackim Bernier. Polar decomposition of semigroups generated by non-selfadjoint quadratic differential operators and regularizing effects. 2019. ⟨hal-02280971⟩

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