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Transactions of the Moscow Mathematical Society

ISSN 1547-738X(online) ISSN 0077-1554(print)



On a method in scattering theory

Authors: È. R. Akchurin and R. A. Minlos
Translated by: V. E. Nazaikinskii
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 72 (2011), vypusk 2.
Journal: Trans. Moscow Math. Soc. 2011, 143-156
MSC (2010): Primary 47A40; Secondary 35P25, 35Q40
Published electronically: January 12, 2012
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Abstract: We use the well-studied Friedrichs model to showcase a new method for proving the asymptotic completeness of two operators, which in our case are the Friedrichs operator $ A$ and the operator obtained from $ A$ by omitting the integral term. Technically, the problem is reduced to a detailed analysis of the Fredholm determinant and minor of an auxiliary integral operator.

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Additional Information

È. R. Akchurin
Affiliation: Mechanics and Mathematics Faculty, Moscow State University, Moscow 119991, Russian Federation

R. A. Minlos
Affiliation: Institute for Information Transmission Problems, Moscow 127994, Russian Federation

Keywords: Asymptotic completeness, Friedrichs model, wave operators, Fredholm minor, Fredholm determinant, stationary phase method.
Published electronically: January 12, 2012
Article copyright: © Copyright 2011 American Mathematical Society