Semigroups for quadratic evolution equations acting on Shubin–Sobolev and Gelfand–Shilov spaces
Keywords:Quadratic evolution equations, Schrödinger equations, semigroups, Sobolev-Shubin spaces, Gelfand-Shilov spaces, ultradistributions
AbstractWe 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.
How to Cite
Wahlberg, P. (2022). Semigroups for quadratic evolution equations acting on Shubin–Sobolev and Gelfand–Shilov spaces. Annales Fennici Mathematici, 47(2), 821–853. https://doi.org/10.54330/afm.119820
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