V. A. Sadovnichii, V. E. Podolskii, “Traces of operators”, Russian Math. Surveys, 61:5 (2006), 885

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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

English version PDF (793 kB) Citations (76) Russian version article

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DOI: https://doi.org/10.1070/RM2006v061n05ABEH004357

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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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:

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
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
Khabir Ishkin, Leysan Davletova, “Regularized Trace of Holomorphic Perturbations of a Spectrally Unstable Operator”, Lobachevskii J Math, 45:6 (2024), 2698
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
Yi-Teng Hu, Murat Şat, “Trace Formulae for Second-Order Differential Pencils with a Frozen Argument”, Mathematics, 11:18 (2023), 3996
I. D. Tsopanov, A. K. Bazzaev, “General Trace Formula for Perturbations from the Gilbert–Shmidt Class”, Lobachevskii J Math, 44:5 (2023), 1938
Dmitry M. Polyakov, “Eigenvalue Asymptotics and a Trace Formula for a Fourth-Order Differential Operator”, Complex Anal. Oper. Theory, 17:8 (2023)
Dmitry M. Polyakov, “Sharp eigenvalue asymptotics of fourth-order differential operators”, ASY, 130:3-4 (2022), 477
Z. Yu. Fazullin, “Trace Formula for a Bounded Perturbation of the Laplace Operator on the Square”, Diff Equat, 58:12 (2022), 1700
Erdal Gül, “On the regularized trace of a differential operator of Sturm-Liouville type”, Filomat, 36:13 (2022), 4515
E. D. Gal'kovskii, A. I. Nazarov, “A trace formula for higher order ordinary differential operators”, Sb. Math., 212:5 (2021), 676–697
Ivanov A.S., “Refining Eigenvalue Estimates For a String With a Singular Weight”, Differ. Equ., 57:10 (2021), 1292–1298
Akhmerova E.F., “Regularized Trace Formula For One Partial Differential Operator”, Azerbaijan J. Math., 11:1 (2021), 45–66
Sen E., “Traces and Inverse Nodal Problems For a Class of Delay Sturm & Ndash;Liouville Operators”, Turk. J. Math., 45:1 (2021), 305–318
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
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
Manafov M.D., “A Regularized Trace Formula For “Weighted” Sturm-Liouville Equation With Point Delta- Interaction”, Turk. J. Math., 45:4 (2021), 1767–1774
Pedro Freitas, Jiří Lipovský, “A Gelfand-Levitan trace formula for generic quantum graphs”, Anal.Math.Phys., 11:2 (2021)
L. A. Takhtajan, “Etudes of the resolvent”, Russian Math. Surveys, 75:1 (2020), 147–186
Guliyev N.J., “Essentially Isospectral Transformations and Their Applications”, Ann. Mat. Pura Appl., 199:4 (2020), 1621–1648

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	3654
Russian version PDF:	2192
English version PDF:	114
References:	137
First page:	20

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