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arXiv · 1910.10955

Semigroups for quadratic evolution equations acting on Shubin-Sobolev and Gelfand-Shilov spaces

Patrik Wahlberg
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Abstract

We consider the initial value Cauchy problem for a class of evolution equations whose Hamiltonian is the Weyl quantization of a homogeneous quadratic form with non-negative definite real part. The solution semigroup is shown to be strongly continuous on several spaces: the Shubin--Sobolev spaces, the Schwartz space, the tempered distributions, the equal index Beurling type Gelfand--Shilov spaces and their dual ultradistribution spaces.

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Patrik Wahlberg. 2019-10-24. Semigroups for quadratic evolution equations acting on Shubin-Sobolev and Gelfand-Shilov spaces. https://arxiv.org/abs/1910.10955

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