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Mat. Sb., 2005, Volume 196, Number 12, Pages 123–156 (Mi msb1445)  

This article is cited in 6 scientific papers (total in 6 papers)

Non-nuclear perturbations of discrete operators and trace formulae

Kh. Kh. Murtazin, Z. Yu. Fazullin

Bashkir State University

Abstract: A trace formula is obtained for unbounded discrete operators perturbed by a Hilbert–Schmidt operator; this formula may be called the discrete analogue of M. Krein's formula for nuclear perturbations. A regularized trace formula of Krein's type is also proved for perturbations in the class $S^p$, $2<p\in\mathbb N$, for arbitrary compact and relatively compact perturbations depending on the behaviour at infinity of the distribution function of the spectrum of the unperturbed operator.

DOI: https://doi.org/10.4213/sm1445

Full text: PDF file (395 kB)
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English version:
Sbornik: Mathematics, 2005, 196:12, 1841–1874

Bibliographic databases:

UDC: 517.94
MSC: Primary 47A55; Secondary 47A10, 47B07, 47B10, 47B25
Received: 31.01.2005 and 24.05.2005

Citation: Kh. Kh. Murtazin, Z. Yu. Fazullin, “Non-nuclear perturbations of discrete operators and trace formulae”, Mat. Sb., 196:12 (2005), 123–156; Sb. Math., 196:12 (2005), 1841–1874

Citation in format AMSBIB
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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. V. A. Sadovnichii, V. E. Podolskii, “Traces of operators”, Russian Math. Surveys, 61:5 (2006), 885–953  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. I. D. Tsopanov, “Obschie formuly regulyarizovannykh sledov dlya integro-differentsialnykh operatorov”, Vladikavk. matem. zhurn., 9:4 (2007), 32–48  mathnet  mathscinet
    3. Kh. Kh. Murtazin, V. A. Sadovnichii, R. Z. Tul'kubaev, “Spectral asymptotics and trace formulas for differential operators with unbounded coefficients”, Differ. Equ., 44:12 (2008), 1691–1700  crossref  mathscinet  zmath  isi  elib
    4. Kh. Kh. Murtazin, “Asymptotic behavior of the spectrum of perturbed fractional powers of differential operators”, Dokl. Math., 77:2 (2008), 198–202  crossref  mathscinet  zmath  isi  elib  elib
    5. Kh. Kh. Murtazin, Z. Yu. Fazullin, “Formula of the regularized trace for perturbation in the Schatten–von Neumann of discrete operators”, Ufa Math. Journal, 7:4 (2015), 104–110  mathnet  crossref  elib
    6. Kanguzhin B.E., Tokmagambetov N.E., “On regularized trace formulas for a well-posed perturbation of the m-Laplace operator”, Differ. Equ., 51:12 (2015), 1583–1588  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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