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Russian Mathematical Surveys, 2006, Volume 61, Issue 5, Pages 885–953
DOI: https://doi.org/10.1070/RM2006v061n05ABEH004357
(Mi rm4833)
 

This article is cited in 76 scientific papers (total in 76 papers)

Traces of operators

V. A. Sadovnichii, V. E. Podolskii

M. V. Lomonosov Moscow State University
References:
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.
Received: 23.04.2006
Bibliographic databases:
Document Type: Article
UDC: 517.984
MSC: Primary 47A55; Secondary 34L10, 47A10, 34B24, 40G10
Language: English
Original paper language: Russian
Citation: V. A. Sadovnichii, V. E. Podolskii, “Traces of operators”, Russian Math. Surveys, 61:5 (2006), 885–953
Citation in format AMSBIB
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\by V.~A.~Sadovnichii, V.~E.~Podolskii
\paper Traces of operators
\jour Russian Math. Surveys
\yr 2006
\vol 61
\issue 5
\pages 885--953
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Linking options:
  • https://www.mathnet.ru/eng/rm4833
  • https://doi.org/10.1070/RM2006v061n05ABEH004357
  • https://www.mathnet.ru/eng/rm/v61/i5/p89
  • This publication is cited in the following 76 articles:
    1. E. F. Akhmerova, M. A. Rakhmatzoda, T. G. Amangildin, “Formula regulyarizovannogo sleda differentsialnogo operatora $2m$-go poryadka s periodicheskimi granichnymi usloviyami”, Izv. vuzov. Matem., 2024, no. 5, 85–90  mathnet  crossref
    2. E. F. Akhmerova, M. A. Rahmatzoda, T. G. Amangildin, “Formula for Regularized Trace of 2m-Order Differential Operator with Periodic Boundary Conditions”, Russ Math., 68:5 (2024), 72  crossref
    3. Khabir Ishkin, Leysan Davletova, “Regularized Trace of Holomorphic Perturbations of a Spectrally Unstable Operator”, Lobachevskii J Math, 45:6 (2024), 2698  crossref
    4. Dmitry M. Polyakov, “Spectral asymptotics and a trace formula for a fourth-order differential operator corresponding to thin film equation”, Monatsh Math, 202:1 (2023), 171  crossref
    5. Yi-Teng Hu, Murat Şat, “Trace Formulae for Second-Order Differential Pencils with a Frozen Argument”, Mathematics, 11:18 (2023), 3996  crossref
    6. I. D. Tsopanov, A. K. Bazzaev, “General Trace Formula for Perturbations from the Gilbert–Shmidt Class”, Lobachevskii J Math, 44:5 (2023), 1938  crossref
    7. Dmitry M. Polyakov, “Eigenvalue Asymptotics and a Trace Formula for a Fourth-Order Differential Operator”, Complex Anal. Oper. Theory, 17:8 (2023)  crossref
    8. Dmitry M. Polyakov, “Sharp eigenvalue asymptotics of fourth-order differential operators”, ASY, 130:3-4 (2022), 477  crossref
    9. Z. Yu. Fazullin, “Trace Formula for a Bounded Perturbation of the Laplace Operator on the Square”, Diff Equat, 58:12 (2022), 1700  crossref
    10. Erdal Gül, “On the regularized trace of a differential operator of Sturm-Liouville type”, Filomat, 36:13 (2022), 4515  crossref
    11. E. D. Gal'kovskii, A. I. Nazarov, “A trace formula for higher order ordinary differential operators”, Sb. Math., 212:5 (2021), 676–697  mathnet  crossref  crossref  zmath  adsnasa  isi  elib
    12. Ivanov A.S., “Refining Eigenvalue Estimates For a String With a Singular Weight”, Differ. Equ., 57:10 (2021), 1292–1298  crossref  mathscinet  isi
    13. Akhmerova E.F., “Regularized Trace Formula For One Partial Differential Operator”, Azerbaijan J. Math., 11:1 (2021), 45–66  mathscinet  isi
    14. Sen E., “Traces and Inverse Nodal Problems For a Class of Delay Sturm & Ndash;Liouville Operators”, Turk. J. Math., 45:1 (2021), 305–318  crossref  mathscinet  isi  scopus
    15. Aliev A.R. Manafov M.D., “Trace Formula For a Sturm-Liouville Operator With a Delta `-Interaction Point”, Differ. Equ., 57:5 (2021), 563–569  crossref  mathscinet  isi
    16. Sen E., “Spectrum, Trace and Nodal Points of a Sturm-Liouville Type Delayed Differential Operator With Interface Conditions”, Rocky Mt. J. Math., 51:1 (2021), 283–294  crossref  mathscinet  isi
    17. Manafov M.D., “A Regularized Trace Formula For “Weighted” Sturm-Liouville Equation With Point Delta- Interaction”, Turk. J. Math., 45:4 (2021), 1767–1774  crossref  mathscinet  isi
    18. Pedro Freitas, Jiří Lipovský, “A Gelfand-Levitan trace formula for generic quantum graphs”, Anal.Math.Phys., 11:2 (2021)  crossref
    19. L. A. Takhtajan, “Etudes of the resolvent”, Russian Math. Surveys, 75:1 (2020), 147–186  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    20. Guliyev N.J., “Essentially Isospectral Transformations and Their Applications”, Ann. Mat. Pura Appl., 199:4 (2020), 1621–1648  crossref  mathscinet  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    References:137
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