期刊
MATHEMATISCHE ZEITSCHRIFT
卷 259, 期 2, 页码 363-391出版社
SPRINGER
DOI: 10.1007/s00209-007-0230-4
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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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