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Mat. Sb., 2002, Volume 193, Number 2, Pages 129–152 (Mi msb630)  

This article is cited in 31 scientific papers (total in 31 papers)

Traces of operators with relatively compact perturbations

V. A. Sadovnichii, V. E. Podolskii

M. V. Lomonosov Moscow State University

Abstract: Regularized trace formulae are proved for abstract operators with a perturbing operator $B$ subordinate to the non-perturbed operator $A_0$ in the following sense: $BA_0^{-1}$ is a compact operator in some Schatten–von Neumann class of finite order. Two essentially different cases can be distinguished here: the resolvent of $A_0$ is either of trace class or not. Five theorems describing various cases of operator subordination and the structure of the spectrum of the unperturbed operator are proved.


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English version:
Sbornik: Mathematics, 2002, 193:2, 279–302

Bibliographic databases:

UDC: 517.94
MSC: Primary 47A55, 47B99; Secondary 47F05
Received: 25.04.2001

Citation: V. A. Sadovnichii, V. E. Podolskii, “Traces of operators with relatively compact perturbations”, Mat. Sb., 193:2 (2002), 129–152; Sb. Math., 193:2 (2002), 279–302

Citation in format AMSBIB
\by V.~A.~Sadovnichii, V.~E.~Podolskii
\paper Traces of operators with relatively compact perturbations
\jour Mat. Sb.
\yr 2002
\vol 193
\issue 2
\pages 129--152
\jour Sb. Math.
\yr 2002
\vol 193
\issue 2
\pages 279--302

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    This publication is cited in the following articles:
    1. Sadovnichii V.A., Podol'skii V.E., Bobrov A.N., “Regularized traces of operators defined by sesquilinear forms”, Dokl. Math., 68:1 (2003), 40–41  mathnet  mathscinet  mathscinet  zmath  isi  elib
    2. Belov S.M., Rybkin A.V., “Higher order trace formulas of the Buslaev-Faddeev-type for the half-line Schrödinger operator with long-range potentials”, J. Math. Phys., 44:7 (2003), 2748–2761  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    3. O. A. Torshina, “O slede differentsialnogo operatora s potentsialom na proektivnoi ploskosti”, Vestnik ChelGU, 2003, no. 9, 178–191  mathnet
    4. Kh. Kh. Murtazin, Z. Yu. Fazullin, “Non-nuclear perturbations of discrete operators and trace formulae”, Sb. Math., 196:12 (2005), 1841–1874  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. D. N. Mikhaskiv, “The regularized trace of an ordinary linear differential operator with polynomial coefficients in $L_2(-\infty,+\infty)$”, Russian Math. Surveys, 60:2 (2005), 361–362  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. Sadovnichii V.A., Podol'skii V.E., “Regularized traces of discrete operators”, Russ. J. Math. Phys., 12:4 (2005), 497–506  mathscinet  zmath  isi  elib
    7. 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
    8. V. A. Sadovnichii, V. E. Podolskii, “Regularized traces of discrete operators”, Proc. Steklov Inst. Math. (Suppl.), 255, suppl. 2 (2006), S161–S177  mathnet  crossref  mathscinet  zmath  elib
    9. Djakov P., Mityagin B., “Trace formula and Spectral Riemann Surfaces for a class of tri-diagonal matrices”, J. Approx. Theory, 139:1-2 (2006), 293–326  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    10. Makin A.S., “Trace formulas for the Sturm-Liouville operator with regular boundary conditions”, Dokl. Math., 76:2 (2007), 702–707  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    11. Bayramoğlu M., Şahintürk H., “Higher order regularized trace formula for the regular Sturm-Liouville equation contained spectral parameter in the boundary condition”, Appl. Math. Comput., 186:2 (2007), 1591–1599  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    12. A. I. Kozko, A. S. Pechentsov, “Regularized Traces of Higher-Order Singular Differential Operators”, Math. Notes, 83:1 (2008), 37–37  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    13. N. M. Aslanova, “A trace formula of a boundary value problem for the operator Sturm–Liouville equation”, Siberian Math. J., 49:6 (2008), 959–967  mathnet  crossref  mathscinet  isi  elib
    14. Sadovnichii V.A., Podol'skii V.E., “Traces of operators with a relatively compact perturbation”, Differ. Equ., 44:5 (2008), 712–716  crossref  mathscinet  zmath  isi  elib  elib  scopus
    15. Sadovnichii V.A., Podol'skii V.E., “Traces of differential operators”, Differ. Equ., 45:4 (2009), 477–493  crossref  mathscinet  zmath  isi  elib  elib  scopus
    16. Bayramov A., Oer Z., Baykal O., “On identity for eigenvalues of second order differential operator equation”, Math. Comput. Modelling, 49:3-4 (2009), 403–412  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    17. N. M. Aslanova, “About the spectrum and the trace formula for the operator Bessel equation”, Siberian Math. J., 51:4 (2010), 569–583  mathnet  crossref  mathscinet  isi  elib  elib
    18. Bairamogly M., Aslanova N.M., “Distribution of Eigenvalues and Trace Formula for the Sturm-Liouville Operator Equation”, Ukrainian Math J, 62:7 (2010), 1005–1017  crossref  mathscinet  zmath  isi  scopus  scopus
    19. È. F. Akhmerova, “Asymptotics of the Spectrum of Nonsmooth Perturbations of Differential Operators of Order $2m$”, Math. Notes, 90:6 (2011), 813–823  mathnet  crossref  crossref  mathscinet  isi
    20. Bayramoglu M., Aslanova N., “Trace of a Problem with Spectral Parameter Dependent Boundary Condition”, Hacet J Math Stat, 40:5 (2011), 635–647  mathscinet  zmath  isi
    21. Aslanova N.M., “Study of the asymptotic eigenvalue distribution and trace formula of a second order operator-differential equation”, Bound Value Probl, 2011, 7  crossref  mathscinet  zmath  isi
    22. Kh. Kh. Murtazin, Z. Yu. Fazullin, “Formula of the regularized trace for perturbation in the Schatten–von Neumann of discrete operators”, Ufa Math. J., 7:4 (2015), 104–110  mathnet  crossref  isi  elib
    23. 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
    24. Intissar A., “Regularized Trace Formula of Magic Gribov Operator on Bargmann Space”, J. Math. Anal. Appl., 437:1 (2016), 59–70  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    25. Movsumova H.F., “Formula For Second Regularized Trace of the Sturm-Liouville Equation With Spectral Parameter in the Boundary Conditions”, Proc. Inst. Math. Mech., 42:1 (2016), 93–105  mathscinet  zmath  isi
    26. E. V. Kirillov, “The spectral identity for the operator with non-nuclear resolvent”, J. Comp. Eng. Math., 4:1 (2017), 69–75  mathnet  crossref  mathscinet  elib
    27. E. V. Kirillov, G. A. Zakirova, “A direct spectral problem for $L$-spectrum of the perturbed operator with a multiple spectrum”, J. Comp. Eng. Math., 4:3 (2017), 19–26  mathnet  crossref  mathscinet  elib
    28. E. V. Kirillov, G. A. Zakirova, “Spectral problem for a mathematical model of hydrodynamics”, J. Comp. Eng. Math., 5:1 (2018), 51–56  mathnet  crossref  mathscinet  elib
    29. Aslanova N.M., Bayramoglu M., Aslanov Kh.M., “Eigenvalue Problem Associated With the Fourth Order Differential-Operator Equation”, Rocky Mt. J. Math., 48:6 (2018), 1763–1779  crossref  mathscinet  zmath  isi  scopus
    30. Aslanova N.M., Bayramoglu M., Aslanov Kh.M., “On One Class Eigenvalue Problem With Eigenvalue Parameter in the Boundary Condition At One End-Point”, Filomat, 32:19 (2018), 6667–6674  crossref  mathscinet  isi  scopus
    31. Fazullin Z.Yu. Nugaeva I.G., “Spectrum and a Trace Formula For a Compactly Supported Perturbation of the 2D Harmonic Oscillator in a Strip”, Differ. Equ., 55:5 (2019), 677–687  crossref  mathscinet  zmath  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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