Rocky Mountain Journal of Mathematics

Spectral properties of the simple layer potential type operators

Milutin R. Dostanić

Full-text: Open access

Article information

Rocky Mountain J. Math., Volume 43, Number 3 (2013), 855-875.

First available in Project Euclid: 1 August 2013

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47B06: Riesz operators; eigenvalue distributions; approximation numbers, s- numbers, Kolmogorov numbers, entropy numbers, etc. of operators
Secondary: 31A10: Integral representations, integral operators, integral equations methods

Simple layer potential asymptotics of singular values


Dostanić, Milutin R. Spectral properties of the simple layer potential type operators. Rocky Mountain J. Math. 43 (2013), no. 3, 855--875. doi:10.1216/RMJ-2013-43-3-855.

Export citation


  • J.M. Anderson, D. Khavinson and V. Lomonosov, Spectral properties of some integral operators arising in potential theory, Quart. J. Math. Oxford 43 (1992), 387-407.
  • J. Arazy and D. Khavinson, Spectral estimates of Cauchy's transform in $L^{2}(\Omega)$, Int. Eq. Oper. Theor. 15 (1992), 901-919.
  • M.Š. Birman and M.Z. Solomjak, Asymptotic behavior of the spectrum of weakly polar integral operators, Izv. Akad. Nauk. 34 (1970), 1151-1168.
  • –––, Estimates of singular values of the integral operators, Uspek. Mat. Nauk. 32 (1977), 17-83.
  • M.R. Dostanić, Spectral properties of the Cauchy operator and its product with Bergman's projection on a bounded domain, Proc. Lond. Math. Soc. 76 (1998), 667-684.
  • M.R. Dostanić, Asymptotic behavior of the singular values fractional integral operators, J. Math. Anal. Appl. 175 (1993), 380-391.
  • –––, Exact asymptotic behavior of the singular values of integral operators with the kernel having singularity on the diagonal, Publ. L'Institut Math. 60 (1996), 45-64.
  • I.C. Gohberg and M.G. Krein, Introduction to the theory of linear nonselfadjoint operators, American Mathematical Society, Providence, R.I., 1969.
  • O.D. Kellog, Foundations of potential theory, Springer, Berlin, 1929.
  • D. Khavinson, M. Putinar and H. Shapiro, On Poincare's variational problem in potential theory, Arch. Rat. Mech. Anal. 185 (2007), 143-184.
  • C. Miranda, Partial differential equations of elliptic type, Second edition, Springer-Verlag, Berlin, 1970.
  • V.I. Paraska, On asymptotics of eigenvalues and singular numbers of linear operators which increase smoothness, Math. SB. 68 (1965), 623-631 (in Russian).
  • S.G. Samko, A.A. Kilbas and O.I. Maricev, Fractional integrals and derivations and some applications, Minsk, 1987 (in Russian).
  • V.S. Vladimirov, Equations of mathematical physics, Moscow, 1981 (in Russian).
  • J. Weidmann, Linear operators in Hilbert space, Springer-Verlag, New York, 1980.
  • H. Widom, Asymptotic behavior of the eigenvalues of certain integral equations, Trans. Amer. Math. Soc. 109 (1963), 278-295. \noindentstyle