Abstract
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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Pravda-Starov, K. Contraction semigroups of elliptic quadratic differential operators. Math. Z. 259, 363–391 (2008). https://doi.org/10.1007/s00209-007-0230-4
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DOI: https://doi.org/10.1007/s00209-007-0230-4