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Trudy Moskovskogo Matematicheskogo Obshchestva, 2011, Volume 72, Issue 2, Pages 189–205 (Mi mmo15)  
On a method in scattering theory

E. R. Akchurina, R. A. Minlosb

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow
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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.
Key words and phrases: asymptotic completeness, Friedrichs model, wave operators, Fredholm minor, Fredholm determinant, stationary phase method.
Received: 11.02.2011
English version:
Transactions of the Moscow Mathematical Society, 2011, Volume 72, Pages 143–156
DOI: https://doi.org/10.1090/S0077-1554-2012-00194-0
Bibliographic databases:
Document Type: Article
UDC: 517.98
MSC: 47A40, 35P25, 35Q40
Language: Russian
Citation: E. R. Akchurin, R. A. Minlos, “On a method in scattering theory”, Tr. Mosk. Mat. Obs., 72, no. 2, MCCME, Moscow, 2011, 189–205; Trans. Moscow Math. Soc., 72 (2011), 143–156
Citation in format AMSBIB
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\by E.~R.~Akchurin, R.~A.~Minlos
\paper On a method in scattering theory
\serial Tr. Mosk. Mat. Obs.
\yr 2011
\vol 72
\issue 2
\pages 189--205
\publ MCCME
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/mmo15}
\zmath{https://zbmath.org/?q=an:06026275}
\elib{https://elibrary.ru/item.asp?id=21369340}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2011
\vol 72
\pages 143--156
\crossref{https://doi.org/10.1090/S0077-1554-2012-00194-0}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84960092195}
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