Trace class properties of the non homogeneous linear Vlasov–Poisson equation in dimension 1+1

We consider the abstract scattering structure of the non homogeneous linearized Vlasov–Poisson equations from the viewpoint of trace class properties which are emblematic of the abstract scattering theory [13, 14, 15, 19]. In dimension 1+1, we derive an original reformulation which is trace class. I...

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Bibliographic Details
Published inJournal of spectral theory Vol. 11; no. 2; pp. 709 - 742
Main Author Despres, Bruno
Format Journal Article
LanguageEnglish
Published European Mathematical Society Publishing House 01.01.2021
European Mathematical Society
Subjects
Differential equations, Linear
Mathematical Physics
Mathematical research
Mathematics
Operator theory
Scattering theory
Spectral Theory
France
linear Vlasov-Poisson
Trace class
wave operators
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ISSN1664-039X
1664-0403
DOI10.4171/jst/354

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Summary:We consider the abstract scattering structure of the non homogeneous linearized Vlasov–Poisson equations from the viewpoint of trace class properties which are emblematic of the abstract scattering theory [13, 14, 15, 19]. In dimension 1+1, we derive an original reformulation which is trace class. It yields the existence of the Moller wave operators. The non homogeneous background electric field is periodic with 4 + \varepsilon bounded derivatives.
ISSN:1664-039X
1664-0403
DOI:10.4171/jst/354