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

This article is cited in 52 scientific papers (total in 52 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.

DOI: https://doi.org/10.4213/rm4833

Full text: PDF file (1069 kB)
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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

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Guliyev N.J., “Essentially Isospectral Transformations and Their Applications”, Ann. Mat. Pura Appl.  crossref  isi
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    4. 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
    5. 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
    6. 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
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    13. Koklu K., Albayrak I., Bayramov A., “A regularized trace formula for second order differential operator equations”, Math. Scand., 107:1 (2010), 123–138  crossref  mathscinet  zmath  isi  elib  scopus
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    18. 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
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    21. 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
    22. 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
    23. 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
    24. 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
    25. 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
    26. 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
    27. 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
    28. 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
    29. 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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    32. Nazarov A.I., Stolyarov D.M., Zatitskiy P.B., “The Tamarkin Equiconvergence Theorem and a First-Order Trace Formula For Regular Differential Operators Revisited”, J. Spectr. Theory, 4:2 (2014), 365–389  crossref  mathscinet  zmath  isi  scopus
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    40. Badanin A.V. Korotyaev E.L., “Trace Formulas For the Beam Equation”, Proceedings of the International Conference on Days on Diffraction 2016 (Dd), ed. Motygin O. Kiselev A. Kapitanova P. Goray L. Kazakov A. Kirpichnikova A., IEEE, 2016, 31–35  crossref  isi  scopus
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    42. 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
    43. 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
    44. 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
    45. Hira F. Altinisik N., “A Trace Formula For Discontinuous Eigenvalue Problem”, Filomat, 31:8 (2017), 2425–2431  crossref  mathscinet  isi  scopus
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    47. 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
    48. E. D. Gal'kovskiǐ, A. I. Nazarov, “A general trace formula for the differential operator on a segment with the last coefficient perturbed by a finite signed measure”, St. Petersburg Math. J., 30:3 (2019), 411–427  mathnet  crossref  isi  elib
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