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Algebra i Analiz, 2004, Volume 16, Issue 1, Pages 70–120 (Mi aa591)  

This article is cited in 7 scientific papers (total in 7 papers)

Research Papers

Pairs of selfadjoint operators and their invariants

D. Alpaya, I. Gohbergb

a Department of Mathematics, Ben-Gurion University of the Negev, Israel
b School of Mathematical Sciences, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv, Israel
References:
Abstract: A trace formula is proved for pairs of selfadjoint operators that are close to each other in a certain sense. An important role is played by a function analytic in the open upper half-plane and with positive imaginary part there. This function, called the characteristic function of the pair, coincides with Kreĭn's $Q$-function in the case where the selfadjoint operators are canonical extensions of a common simple and closed Hermitian operator. Special emphasis is given to the finite-dimensional case. Relationships with Kreĭn's spectral shift function are also considered. Finally, the case of canonical differential expressions is discussed briefly. In this case, the function $N$ may be chosen to be the Weyl function of the canonical differential expression.
Received: 24.10.2003
English version:
St. Petersburg Mathematical Journal, 2005, Volume 16, Issue 1, Pages 59–104
DOI: https://doi.org/10.1090/S1061-0022-04-00844-1
Bibliographic databases:
Document Type: Article
UDC: Krein's spectral shift function, the $Q$-function associated with a~symmetric operator, the Weyl function.
Language: English
Citation: D. Alpay, I. Gohberg, “Pairs of selfadjoint operators and their invariants”, Algebra i Analiz, 16:1 (2004), 70–120; St. Petersburg Math. J., 16:1 (2005), 59–104
Citation in format AMSBIB
\Bibitem{AlpGoh04}
\by D.~Alpay, I.~Gohberg
\paper Pairs of selfadjoint operators and their invariants
\jour Algebra i Analiz
\yr 2004
\vol 16
\issue 1
\pages 70--120
\mathnet{http://mi.mathnet.ru/aa591}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2069002}
\zmath{https://zbmath.org/?q=an:1084.47019}
\transl
\jour St. Petersburg Math. J.
\yr 2005
\vol 16
\issue 1
\pages 59--104
\crossref{https://doi.org/10.1090/S1061-0022-04-00844-1}
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  • https://www.mathnet.ru/eng/aa/v16/i1/p70
  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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