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Zapiski Nauchnykh Seminarov POMI, 2011, Volume 389, Pages 5–20 (Mi znsl4115)  
This article is cited in 4 scientific papers (total in 4 papers)

The future and past wave operators on the singular spectrum

R. V. Bessonov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia
Full-text PDF (606 kB) Citations (4)
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Abstract: We consider averaged wave operators constructed for singular unitary operators $U_1$, $U_2$ and a bounded identification operator $A$. In the case of rank-two commutator $AU_1-U_2A$, we show that averaged wave operators of past and future exist or do not exist simultaneously, and if they exist, they must coincide. As a consequence, we obtain some results concerning the boundary behavior of Cauchy-type integrals.
Key words and phrases: wave operator, summation methods, singular spectral measure.
Received: 24.06.2011
English version:
Journal of Mathematical Sciences (New York), 2012, Volume 182, Issue 5, Pages 587–594
DOI: https://doi.org/10.1007/s10958-012-0763-x
Bibliographic databases:
Document Type: Article
UDC: 517.98
Language: Russian
Citation: R. V. Bessonov, “The future and past wave operators on the singular spectrum”, Investigations on linear operators and function theory. Part 39, Zap. Nauchn. Sem. POMI, 389, POMI, St. Petersburg, 2011, 5–20; J. Math. Sci. (N. Y.), 182:5 (2012), 587–594
Citation in format AMSBIB
\Bibitem{Bes11}
\by R.~V.~Bessonov
\paper The future and past wave operators on the singular spectrum
\inbook Investigations on linear operators and function theory. Part~39
\serial Zap. Nauchn. Sem. POMI
\yr 2011
\vol 389
\pages 5--20
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4115}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2012
\vol 182
\issue 5
\pages 587--594
\crossref{https://doi.org/10.1007/s10958-012-0763-x}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84860362557}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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