Journal of Integral Equations and Applications

Autoconvolution equations of the third kind with Abel integral

Lothar Von Wolfersdorf

Full-text: Open access

Article information

Source
J. Integral Equations Applications, Volume 23, Number 1 (2011), 113-136.

Dates
First available in Project Euclid: 22 March 2011

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1300802758

Digital Object Identifier
doi:10.1216/JIE-2011-23-1-113

Mathematical Reviews number (MathSciNet)
MR2781139

Zentralblatt MATH identifier
1219.45002

Subjects
Primary: 45G10: Other nonlinear integral equations
Secondary: 45D05: Volterra integral equations [See also 34A12] 45E10: Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) [See also 47B35] 45M05: Asymptotics

Keywords
Quadratic integral equations autoconvolution equations Abel type integral equations

Citation

Wolfersdorf, Lothar Von. Autoconvolution equations of the third kind with Abel integral. J. Integral Equations Applications 23 (2011), no. 1, 113--136. doi:10.1216/JIE-2011-23-1-113. https://projecteuclid.org/euclid.jiea/1300802758


Export citation

References

  • L. Berg, Asymptotische Darstellungen und Entwicklungen, Deutscher Verlag der Wissenschaften, Berlin, 1968.
  • L. Berg and L.v. Wolfersdorf, On a class of generalized autoconvolution equations of the third kind, Z. Anal. Anw. (J. Anal. Appl.) 24 (2005), 217-250.
  • A. Erdélyi, Asymptotic expansions, Dover Publications, New York, 1956.
  • –––, ed., Higher transcendental functions, Vol. III, McGraw Hill, New York, 1955.
  • B. Hofmann and L.v. Wolfersdorf, On the determination of a density function by its autoconvolution coefficient, Numer. Funct. Anal. Optim. 27 (2006), 357-375.
  • J. Janno, Nonlinear equations with operators satisfying generalized Lipschitz-conditions in scales, Z. Anal. Anw. (J. Anal. Appl.) 18 (1999), 287-295.
  • J. Janno and L.v. Wolfersdorf, A general class of autoconvolution equations of the third kind, Z. Anal. Anw. (J. Anal. Appl.) 24 (2005), 523-543.
  • –––, Integro-differential equations of first order with autoconvolution integral, J. Integral Equations Appl., to appear.
  • L.v. Wolfersdorf, On the theory of convolution equations of the third kind, J. Math. Anal. Appl. 331 (2007), 1314-1336.
  • L.v. Wolfersdorf and B. Hofmann, A specific inverse problem for the Volterra convolution equation, Appl. Anal. 87 (2008), 59-81.
  • L.v. Wolfersdorf and J. Janno, On the theory of convolution equations of the third kind II, J. Math. Anal. Appl. 342 (2008), 838-863.