Geodesic
Semigroups for quadratic evolution equations acting on Shubin–Sobolev and Gelfand–Shilov spaces
Patrik Wahlberg1
1Politecnico 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 
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
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     journal = {Annales Fennici Mathematici},
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