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Uspekhi Mat. Nauk, 2006, Volume 61, Issue 5(371), Pages 89–156 (Mi umn4833)  

This article is cited in 50 scientific papers (total in 50 papers)

Traces of operators

V. A. Sadovnichii, V. E. Podolskii

M. V. Lomonosov Moscow State University

Abstract: This survey is devoted to the history and the current state of the theory of regularized traces of linear operators. The main focus is on operators with discrete spectrum. Several appendices are devoted to closely related areas of spectral theory and to the formulation of some important unsolved problems.


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English version:
Russian Mathematical Surveys, 2006, 61:5, 885–953

Bibliographic databases:

UDC: 517.984
MSC: Primary 47A55; Secondary 34L10, 47A10, 34B24, 40G10
Received: 23.04.2006

Citation: V. A. Sadovnichii, V. E. Podolskii, “Traces of operators”, Uspekhi Mat. Nauk, 61:5(371) (2006), 89–156; Russian Math. Surveys, 61:5 (2006), 885–953

Citation in format AMSBIB
\by V.~A.~Sadovnichii, V.~E.~Podolskii
\paper Traces of operators
\jour Uspekhi Mat. Nauk
\yr 2006
\vol 61
\issue 5(371)
\pages 89--156
\jour Russian Math. Surveys
\yr 2006
\vol 61
\issue 5
\pages 885--953

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    This publication is cited in the following articles:
    1. I. D. Tsopanov, “Obschie formuly regulyarizovannykh sledov dlya integro-differentsialnykh operatorov”, Vladikavk. matem. zhurn., 9:4 (2007), 32–48  mathnet  mathscinet
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    3. V. A. Sadovnichii, V. E. Podol'skii, “Traces of operators with a relatively compact perturbation”, Differ. Equ., 44:5 (2008), 712–716  crossref  mathscinet  zmath  isi  elib  elib  scopus
    4. S. A. Stepin, “Parametrix, kernel asymptotics, and regularized trace for the diffusion semigroup”, Dokl. Math., 77:3 (2008), 424–427  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    5. R. S. Ismagilov, A. G. Kostyuchenko, “Perturbation of the Spectrum of a Differential Operator under a Bounded Perturbation of the Potential”, Funct. Anal. Appl., 43:3 (2009), 208–216  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. Kh. Kh. Murtazin, Z. Yu. Fazullin, “Spectrum and the trace formula for a two-dimensional Schrödinger operator in a homogeneous magnetic field”, Differ. Equ., 45:4 (2009), 564–579  crossref  mathscinet  zmath  isi  elib  elib  scopus
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    15. Bayramoglu M., Aslanova N., “Formula for second regularized trace of a problem with spectral parameter dependent boundary condition”, Hacet. J. Math. Stat., 40:5 (2011), 635–647  mathscinet  zmath  isi
    16. Osipov A., “On a G. Boole's identity for rational functions and some trace formulas”, Complex Anal. Oper. Theory, 5:3 (2011), 889–900  crossref  mathscinet  zmath  isi  elib  scopus
    17. Aslanova N.M., “Study of the asymptotic eigenvalue distribution and trace formula of a second order operator-differential equation”, Bound. Value Probl., 2011 (2011), 7, 22 pp.  crossref  mathscinet  zmath  isi
    18. Dostanić M.R., “Regularized trace of the inverse of the Dirichlet Laplacian”, Comm. Pure Appl. Math., 64:8 (2011), 1148–1164  crossref  mathscinet  zmath  isi  scopus
    19. Yang Chuan-Fu, “Trace formulae for the matrix Schrödinger equation with energy-dependent potential”, Journal of Mathematical Analysis and Applications, 2012  crossref  mathscinet  isi  scopus
    20. M. K. Kerimov, “The theory of regularized traces of operators as applied to approximate computation of eigenvalues and eigenfunctions of fluid dynamics problems”, Comput. Math. Math. Phys., 52:5 (2012), 756–786  mathnet  crossref  mathscinet  isi  elib  elib
    21. M. K. Kerimov, “Approximate computation of eigenvalues and eigenfunctions of Sturm–Liouville differential operators by applying the theory of regularized traces”, Comput. Math. Math. Phys., 52:3 (2012), 351–386  mathnet  crossref  zmath  adsnasa  isi  elib  elib
    22. S. I. Kadchenko, S. N. Kakushkin, “Vychislenie znachenii sobstvennykh funktsii diskretnykh poluogranichennykh snizu operatorov metodom regulyarizovannykh sledov”, Vestn. SamGU. Estestvennonauchn. ser., 2012, no. 6(97), 13–21  mathnet
    23. Aslanova N.M., “The Asymptpotics of Eigenvalues and Trace Formula of Operator Associated with One Singular Problem”, Bound. Value Probl., 2012, 1–12  crossref  mathscinet  isi  scopus
    24. S. I. Kadchenko, S. N. Kakushkin, “Chislennye metody nakhozhdeniya sobstvennykh chisel i sobstvennykh funktsii vozmuschennykh samosopryazhennykh operatorov”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2012, no. 13, 45–57  mathnet
    25. Bayramov A. Caliskan S.K. Akgun F.A., “The Second Regularized Trace of Differential Operator Equation with the Semi-Periodic Boundary Conditions”, Math. Meth. Appl. Sci., 35:18 (2012), 2185–2197  crossref  mathscinet  zmath  isi  elib  scopus
    26. Kh. K. Ishkin, “On analytic properties of Weyl function of Sturm–Liouville operator with a decaying complex potential”, Ufa Math. J., 5:1 (2013), 36–55  mathnet  crossref  mathscinet  elib
    27. Yang Ch.-F., “Trace for Differential Pencils on a Star-Type Graph”, Z. Naturfors. Sect. A-J. Phys. Sci., 68:6-7 (2013), 421–426  crossref  mathscinet  isi  elib  scopus
    28. Badanin A., Korotyaev E., “Trace Formula for Fourth Order Operators on the Circle”, Dyn. Partial Differ. Equ., 10:4 (2013), 343–352  crossref  mathscinet  zmath  isi  scopus
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    30. Aslanova N.M., Bairamogly M., “On Generalized Regularized Trace of a Fourth-Order Differential Operator With Operator Coefficient”, Ukr. Math. J., 66:1 (2014), 145–152  crossref  mathscinet  zmath  isi  scopus
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    32. Dostanic M.R., “Regularized Trace of the Operator of Riesz Potential Type on Bounded Domain in C”, Adv. Math., 272 (2015), 330–349  crossref  mathscinet  zmath  isi  scopus
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    40. A. I. Kozko, “O nekotorykh priznakakh skhodimosti dlya znakopostoyannykh i znakochereduyuschikhsya ryadov”, Chebyshevskii sb., 18:1 (2017), 123–133  mathnet  crossref  elib
    41. A. S. Ivanov, A. M. Savchuk, “Trace of Order $(-1)$ for a String with Singular Weight”, Math. Notes, 102:2 (2017), 164–180  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    42. Sen E., “A Regularized Trace Formula and Oscillation of Eigenfunctions of a Sturm-Liouville Operator With Retarded Argument At 2 Points of Discontinuity”, Math. Meth. Appl. Sci., 40:18 (2017), 7051–7061  crossref  mathscinet  zmath  isi  scopus
    43. Bayramoglu M. Bayramov A. Sen E., “A Regularized Trace Formula For a Discontinuous Sturm-Liouville Operator With Delayed Argument”, Electron. J. Differ. Equ., 2017, 104  mathscinet  zmath  isi
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    45. Hira F., “A Trace Formula For the Sturm-Liouville Type Equation With Retarded Argument”, Commun. Fac. Sci. Univ. Ank.-Ser, A1 Math. Stat, 66:1 (2017), 124–132  crossref  mathscinet  zmath  isi
    46. Aslanova N.M., Bayramoglu M., Aslanov Kh.M., “Some Spectral Properties of Fourth Order Differential Operator Equation”, Oper. Matrices, 12:1 (2018), 287–299  crossref  mathscinet  zmath  isi  scopus
    47. E. D. Galkovskii, A. I. Nazarov, “Obschaya formula sledov dlya differentsialnogo operatora na otrezke pri vozmuschenii mladshego koeffitsienta konechnym zaryadom”, Algebra i analiz, 30:3 (2018), 30–54  mathnet  elib
    48. A. S. Ivanov, “Traces of higher negative orders for a string with a singular weight”, Differ. Equ., 54:10 (2018), 1310–1320  crossref  crossref  mathscinet  zmath  isi  elib  scopus
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    50. Akgun F.A. Bayramoglu M. Bayramov A., “The Second Regularized Trace Formula For the Sturm-Liouville Operator”, Miskolc Math. Notes, 20:1 (2019), 17–32  crossref  isi
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