Contraction semigroups of elliptic quadratic differential operators

Details Contraction semigroups of elliptic quadratic differential operators Contraction semigroups of elliptic quadratic differential operators

2007-05-07

arxiv.org/abs/0705.0950v1

Mathematics

Analysis of PDEs

26 pages

Scientific paper

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.

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