Geodesic
Semigroups for quadratic evolution equations acting on Shubin–Sobolev and Gelfand–Shilov spaces
Patrik Wahlberg1
1 Politecnico di Torino, Dipartimento di Scienze Matematiche
Annales Fennici Mathematici, Tome 47 (2022) no. 2, pp. 821-853.

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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.
DOI : 10.54330/afm.119820
Keywords: Quadratic evolution equations, Schrödinger equations, semigroups, Sobolev-Shubin spaces, Gelfand-Shilov spaces, ultradistributions

Patrik Wahlberg 1

1 Politecnico di Torino, Dipartimento di Scienze Matematiche 
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Patrik Wahlberg. Semigroups for quadratic evolution equations acting on Shubin–Sobolev and Gelfand–Shilov spaces. Annales Fennici Mathematici, Tome 47 (2022) no. 2, pp. 821-853. doi : 10.54330/afm.119820. http://geodesic.mathdoc.fr/articles/10.54330/afm.119820/

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