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Mathematics of the USSR-Izvestiya, 1970, Volume 4, Issue 5, Pages 1151–1168
DOI: https://doi.org/10.1070/IM1970v004n05ABEH000948
(Mi im2462)
 

This article is cited in 24 scientific papers (total in 24 papers)

Asymptotic behavior of the spectrum of weakly polar integral operators

M. Sh. Birman, M. Z. Solomyak
References:
Abstract: The principal term is calculated for an asymptotic expression for the spectrum of multidimensional symmetric integral operators of potential type.
Received: 16.03.1970
Bibliographic databases:
UDC: 517.43
Language: English
Original paper language: Russian
Citation: M. Sh. Birman, M. Z. Solomyak, “Asymptotic behavior of the spectrum of weakly polar integral operators”, Math. USSR-Izv., 4:5 (1970), 1151–1168
Citation in format AMSBIB
\Bibitem{BirSol70}
\by M.~Sh.~Birman, M.~Z.~Solomyak
\paper Asymptotic behavior of the spectrum of weakly polar integral
operators
\jour Math. USSR-Izv.
\yr 1970
\vol 4
\issue 5
\pages 1151--1168
\mathnet{http://mi.mathnet.ru//eng/im2462}
\crossref{https://doi.org/10.1070/IM1970v004n05ABEH000948}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=279638}
\zmath{https://zbmath.org/?q=an:0261.47027}
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  • https://doi.org/10.1070/IM1970v004n05ABEH000948
  • https://www.mathnet.ru/eng/im/v34/i5/p1142
  • This publication is cited in the following 24 articles:
    1. D. V. Zanin, F. A. Sukochev, “Connes integration formula: a constructive approach”, Funct. Anal. Appl., 57:1 (2023), 40–59  mathnet  crossref  crossref
    2. Alexander Nazarov, Yulia Petrova, “L2-small ball asymptotics for Gaussian random functions: A survey”, Probab. Surveys, 20:none (2023)  crossref
    3. G. Rozenblum, G. Tashchiyan, “Spectral Estimates and Asymptotics for Integral Operators on Singular Sets”, J Math Sci, 268:4 (2022), 493  crossref
    4. A. V. Sobolev, “On the spectrum of the one-particle density matrix”, Funct. Anal. Appl., 55:2 (2021), 113–121  mathnet  crossref  crossref  isi
    5. Chigansky P., Kleptsyna M., “Sharp Asymptotics in a Fractional Sturm-Liouville Problem”, Fract. Calc. Appl. Anal., 24:3 (2021), 715–738  crossref  isi
    6. U. R. Freiberg, N. V. Rastegaev, “On spectral asymptotics of the sturm–liouville problem with self-conformal singular weight”, Siberian Math. J., 61:5 (2020), 901–912  mathnet  mathnet  crossref  crossref  isi  scopus
    7. Chigansky P., Kleptsyna M., “Exact Asymptotics in Eigenproblems For Fractional Brownian Covariance Operators”, Stoch. Process. Their Appl., 128:6 (2018), 2007–2059  crossref  isi
    8. G. V. Rozenblum, “On the mathematical papers of Mikhail Zakharovich Solomyak”, St. Petersburg Math. J., 30:3 (2019), 391–410  mathnet  crossref  mathscinet  isi  elib
    9. St. Petersburg Math. J., 30:3 (2019), 601–619  mathnet  crossref  mathscinet  isi  elib
    10. Polosin A.A., “On Eigenfunctions of a Convolution Operator on a Finite Interval For Which the Fourier Image of the Kernel Is the Characteristic Function”, Dokl. Math., 96:1 (2017), 389–392  crossref  isi
    11. Polosin A.A., “Spectrum and Eigenfunctions of the Convolution Operator on a Finite Interval With Kernel Whose Transform Is a Characteristic Function”, Differ. Equ., 53:9 (2017), 1145–1159  crossref  isi
    12. N. V. Rastegaev, “On spectral asymptotics of the Neumann problem for the Sturm–Liouville equation with self-similar generalized Cantor type weight”, J. Math. Sci. (N. Y.), 210:6 (2015), 814–821  mathnet  crossref
    13. Milutin R. Dostanić, “Spectral properties of the simple layer potential type operators”, Rocky Mountain J. Math., 43:3 (2013)  crossref
    14. M. Z. Solomyak, T. A. Suslina, D. R. Yafaev, “On the mathematical works of M. Sh. Birman”, St. Petersburg Math. J., 23:1 (2012), 1–38  mathnet  crossref  mathscinet  zmath  isi  elib
    15. A. I. Nazarov, “Logarithmic L2-small ball asymptotics with respect to self-similar measure for some Gaussian processes”, J. Math. Sci. (N. Y.), 133:3 (2006), 1314–1327  mathnet  crossref  mathscinet  zmath  elib
    16. A. I. Nazarov, Ya. Yu. Nikitin, “Logarithmic L2-small ball asymptotics for some fractional Gaussian processes”, Theory Probab. Appl., 49:4 (2005), 645–658  mathnet  crossref  crossref  mathscinet  zmath  isi
    17. M.R. Dostanić, “Spectral Estimates for the Commutator of Two-Dimensional Hilbert Transformation and the Operator of Multiplication with a C1 Function”, Rocky Mountain J. Math., 34:1 (2004)  crossref
    18. B. V. Pal'tsev, “Asymptotic behaviour of the spectra of integral convolution operators on a finite interval with homogeneous polar kernels”, Izv. Math., 67:4 (2003), 695–779  mathnet  crossref  crossref  mathscinet  zmath  isi
    19. A. S. Andreev, “Asymptotics of the spectrum of compact pseudodifferential operators in a Euclidean domain”, Math. USSR-Sb., 65:1 (1990), 205–228  mathnet  crossref  mathscinet  zmath
    20. Harold Widom, Contributions to Operator Theory and its Applications, 1988, 495  crossref
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