Contraction semigroups of elliptic quadratic differential operators

Karel Pravda-Starov (1)

1 Department of Mathematics [Berkeley]

We study the contraction semigroups of elliptic quadratic differential operators. Elliptic quadratic differential operators are the non-selfadjoint operators defined in the Weyl quantization by complex-valued elliptic quadratic symbols. We establish in this paper that under the assumption of ellipticity, as soon as the real part of their Weyl symbols is a non-zero non-positive quadratic form, the norm of contraction semigroups generated by these operators decays exponentially in time.

Mots clés: subellipticity; contraction semigroups; elliptic quadratic differential operators; exponential decay; pseudospectrum; subellipticity.

Domaines: Equations aux dérivées partielles [math.AP]

Karel Pravda-Starov. Contraction semigroups of elliptic quadratic differential operators. 2007. ⟨hal-00145109⟩