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Mat. Sb. (N.S.), 1984, Volume 125(167), Number 3(11), Pages 420–430 (Mi msb2093)  

This article is cited in 10 scientific papers (total in 10 papers)

The spectral shift function for a dissipative and a selfadjoint operator, and trace formulas for resonances

A. V. Rybkin


Abstract: A trace formula is given for an abstract pair consisting of a dissipative operator and a selfadjoint operator, and a connection is established between the spectral shift function of this pair and the corresponding scattering matrix. As a consequence, trace formulas are obtained for a specific dissipative operator arising in the problem of resonance scattering of plane waves on a one-dimensional semi-infinite crystal.
Bibliography: 8 titles.

Full text: PDF file (605 kB)
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English version:
Mathematics of the USSR-Sbornik, 1986, 53:2, 421–431

Bibliographic databases:

UDC: 517.98
MSC: Primary 47A40, 47B10, 47B25, 47B44; Secondary 34B25, 47A10, 47A55
Received: 19.07.1983

Citation: A. V. Rybkin, “The spectral shift function for a dissipative and a selfadjoint operator, and trace formulas for resonances”, Mat. Sb. (N.S.), 125(167):3(11) (1984), 420–430; Math. USSR-Sb., 53:2 (1986), 421–431

Citation in format AMSBIB
\Bibitem{Ryb84}
\by A.~V.~Rybkin
\paper The spectral shift function for a dissipative and a selfadjoint operator, and trace formulas for resonances
\jour Mat. Sb. (N.S.)
\yr 1984
\vol 125(167)
\issue 3(11)
\pages 420--430
\mathnet{http://mi.mathnet.ru/msb2093}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=764904}
\zmath{https://zbmath.org/?q=an:0586.47034|0569.47033}
\transl
\jour Math. USSR-Sb.
\yr 1986
\vol 53
\issue 2
\pages 421--431
\crossref{https://doi.org/10.1070/SM1986v053n02ABEH002930}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Rybkin, “Trace for the pair of a contraction and a unitary operator”, Funct. Anal. Appl., 21:4 (1987), 334–336  mathnet  crossref  mathscinet  zmath  isi
    2. Krein M., “Disturbance Determinants and the Trace Formula for Some Classes of Operator Pairs”, 17, no. 1, 1987, 129–187  mathscinet  zmath  isi
    3. Neidhardt H., “Scattering Matrix and Spectral Shift of the Nuclear Dissipative Scattering-Theory .2.”, 19, no. 1, 1988, 43–62  mathscinet  zmath  isi
    4. Jonas P., “On the Trace Formula of Perturbation-Theory .1.”, Math. Nachr., 137 (1988), 257–281  crossref  mathscinet  zmath  isi
    5. A. V. Rybkin, “The discrete and the singular spectrum in the trace formula for contracting and unitary operators”, Funct. Anal. Appl., 23:3 (1989), 244–246  mathnet  crossref  mathscinet  zmath  isi
    6. Adamjan V. Neidhardt H., “On the Summability of the Spectral Shift Function for Pair of Contractions and Dissipative Operators”, 24, no. 1, 1990, 187–206  mathscinet  zmath  isi
    7. V. A. Lyubishkin, “On the trace formulas of Gel'fand–Levitan and Krein”, Math. USSR-Sb., 74:2 (1993), 531–540  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. A. V. Rybkin, “The spectral shift function, the characteristic function of a contraction, and a generalized integral”, Russian Acad. Sci. Sb. Math., 83:1 (1995), 237–281  mathnet  crossref  mathscinet  zmath  isi
    9. Behrndt J., Malamud M.M., Neidhardt H., “Trace Formulae for Dissipative and Coupled Scattering Systems”, Spectral Theory in Inner Product Spaces and Applications, Operator Theory Advances and Applications, 188, eds. Behrndt J., Forster KH., Langer H., Trunk C., Birkhauser Verlag Ag, 2009, 49–85  mathscinet  zmath  adsnasa  isi
    10. M. M. Malamud, H. Neidhardt, V. V. Peller, “Analytic operator Lipschitz functions in the disk and a trace formula for functions of contractions”, Funct. Anal. Appl., 51:3 (2017), 185–203  mathnet  crossref  crossref  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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