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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Hypercyclicity in the scattering theory for linear transport equation


Author: H. Emamirad
Journal: Trans. Amer. Math. Soc. 350 (1998), 3707-3716
MSC (1991): Primary 47D05; Secondary 82A70
MathSciNet review: 1451598
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Abstract: We show how the hypercyclicity of the transport semigroup can intervene in the scattering theory to characterize the density property of the Lax and Phillips representation theorem and conversely, how the existence of the wave operators of the scattering theory can be used for recovering the hypercyclicity of the absorbing transport group in some weighted $L^{1}$ spaces.


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Additional Information

H. Emamirad
Affiliation: Laboratoire de Modélisation Méchanique et de Mathématiques Appliquées, SP2MI. Université de Poitiers, Boulevard 3, Teleport 2, BP 179. 86 960 FUTUROSCOPE Cedex, France
Email: emamirad@13ma.univ-poitiers.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-98-02062-5
PII: S 0002-9947(98)02062-5
Keywords: Hypercyclic semigroup, Lax and Phillips scattering theory, two similar semigroups
Received by editor(s): October 29, 1996
Article copyright: © Copyright 1998 American Mathematical Society