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Pré-Publication, Document De Travail Année : 2020

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

Résumé

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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Dates et versions

hal-02280971 , version 1 (06-09-2019)
hal-02280971 , version 2 (12-01-2020)
hal-02280971 , version 3 (29-12-2021)

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Paul Alphonse, Joackim Bernier. Polar decomposition of semigroups generated by non-selfadjoint quadratic differential operators and regularizing effects. 2020. ⟨hal-02280971v2⟩
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