RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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.

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

Full text: PDF file (1069 kB)
References: PDF file   HTML file

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
\Bibitem{SadPod06}
\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
\mathnet{http://mi.mathnet.ru/umn4833}
\crossref{https://doi.org/10.4213/rm4833}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2328258}
\zmath{https://zbmath.org/?q=an:1157.47013}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2006RuMaS..61..885S}
\elib{http://elibrary.ru/item.asp?id=25787331}
\transl
\jour Russian Math. Surveys
\yr 2006
\vol 61
\issue 5
\pages 885--953
\crossref{https://doi.org/10.1070/RM2006v061n05ABEH004357}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000244992000002}
\elib{http://elibrary.ru/item.asp?id=13688573}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33947537473}


Linking options:
  • http://mi.mathnet.ru/eng/umn4833
  • https://doi.org/10.4213/rm4833
  • http://mi.mathnet.ru/eng/umn/v61/i5/p89

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


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

    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
    2. 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
    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
    7. Makin A., “Regularized trace of the Sturm-Liouville operator with irregular boundary conditions”, Electron. J. Differential Equations, 2009, no. 27, 27, 8 pp.  mathscinet  zmath  isi  elib
    8. S. A. Stepin, “Schwartz Kernel Asymptotics and Regularized Traces of Diffusion Semigroups”, Funct. Anal. Appl., 44:1 (2010), 76–80  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. M. R. Dostanic, “Spectral asymptotics and the regularized trace of a singular integral operator”, Sb. Math., 201:8 (2010), 1121–1134  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. 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
    11. S. A. Stepin, “Parametrix, heat kernel asymptotics, and regularized trace of the diffusion semigroup”, Proc. Steklov Inst. Math., 271 (2010), 228–245  mathnet  crossref  mathscinet  isi  elib
    12. 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
    13. Albayrak I., Koklu K., Bayramov A., “A regularized trace formula for differential equations with trace class operator coefficients”, Rocky Mountain J. Math., 40:4 (2010), 1095–1110  crossref  mathscinet  zmath  isi  scopus
    14. 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
    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
    29. Dostanic M.R., “Spectral Properties of the Operator of Bessel Potential Type”, J. Math. Anal. Appl., 419:1 (2014), 255–272  crossref  mathscinet  zmath  isi  scopus
    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
    31. 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
    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
    33. I. D. Tsopanov, “General regularized trace formulae for loaded equations”, Ufa Math. J., 7:1 (2015), 70–82  mathnet  crossref  isi  elib
    34. A. O. Shcherbakov, “Regularized Trace of the Dirac Operator”, Math. Notes, 98:1 (2015), 168–179  mathnet  crossref  crossref  mathscinet  isi  elib
    35. R. S. Ismagilov, “Spectral Trace Formula for Local Fields”, Math. Notes, 98:6 (2015), 926–931  mathnet  crossref  crossref  mathscinet  isi  elib
    36. Badanin A., Korotyaev E., “Trace Formulas For Fourth Order Operators on Unit Interval, II”, 12, no. 3, 2015, 217–239  mathscinet  zmath  isi
    37. Intissar A., “Regularized Trace Formula of Magic Gribov Operator on Bargmann Space”, 437, no. 1, 2016, 59–70  crossref  mathscinet  zmath  isi  scopus
    38. Freitas P. Kennedy J.B., “Summation Formula Inequalities For Eigenvalues of the Perturbed Harmonic Oscillator”, Osaka J. Math., 53:2 (2016), 397–416  mathscinet  zmath  isi  elib
    39. 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
    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
    44. Hira F. Altinisik N., “A Trace Formula For Discontinuous Eigenvalue Problem”, Filomat, 31:8 (2017), 2425–2431  crossref  mathscinet  isi  scopus
    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
    49. E. D. Galkovskii, “Formula sleda dlya differentsialnogo operatora vysokogo poryadka na otrezke pri vozmuschenii mladshego koeffitsienta konechnym zaryadom”, Funkts. analiz i ego pril., 53:2 (2019), 64–67  mathnet  crossref  elib
    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
  • Успехи математических наук Russian Mathematical Surveys
    Number of views:
    This page:2663
    Full text:997
    References:92
    First page:20

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019