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

2019/10/24 by Wahlberg, Patrik
#35Q40 #35S11 #42B35 #46E35 #46F05 #47D06 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1910.10955

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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