Journal of Integral Equations and Applications

Distributional Solutions of the Wiener-Hopf Integral and Integro-differential Equations

R. Estrada and R.P. Kanwal

Full-text: Open access

Article information

J. Integral Equations Applications, Volume 3, Number 4 (1991), 489-514.

First available in Project Euclid: 5 June 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Estrada, R.; Kanwal, R.P. Distributional Solutions of the Wiener-Hopf Integral and Integro-differential Equations. J. Integral Equations Applications 3 (1991), no. 4, 489--514. doi:10.1216/jiea/1181075646.

Export citation


  • A. Erdélyi, Asympotic expansions, Dover, New York, 1956.
  • --------, Asymptotic expansions of Fourier integrals involving logarithmic singularities, J. SIAM 4 (1956), 38-47.
  • R. Estrada and R.P. Kanwal, Distributional solutions of singular integral equations, J. Integral Equations 8 (1985), 41-85.
  • --------, Distributional solutions of dual integral equations of Cauchy, Abel, and Tï tchmarsch types, J. Integral Equations 9 (1985), 277-305.
  • --------, Integral equations with logarithmic kernels, IMA J. Applied Math. 43 (1989), 133-155.
  • I.M. Gelfand and G.E. Shilov, Generalized functions, Academic Press, New York, 1964.
  • J. Horváth, Topological vector spaces and distributions, Addison-Wesley, MA, 1966.
  • D.S. Jones, Generalised functions, Cambridge University Press, Cambridge-New York, 1982.
  • R.P. Kanwal, Generalized functions, Academic Press, New York, 1983.
  • M.G. Krein, Integral equation on a half-line with kernels depending upon the difference of the arguments, Amer. Math. Soc. Trans. 22 (1963), 163-288.
  • B. Noble, Methods based on the Wiener-Hopf technique, Pergamon Press, New York, 1958.
  • B. Salsa, Equazioni integrali di Wiener-Hopf in spazi di Besov e applicazioni, Bol. Un. Mat. Ital. B, 5, 14 (1977), 745-760.
  • A.F. Dos Santos and F.S. Teixeira, On a class of Wiener-Hopf equations of the first kind in a Sobolev space, Integral Equations and Operator Theory 10 (1987), 62-81.
  • --------, Theory of a class of Wiener-Hopf equations of the first kind: application to the Sommerfeld problem, J. Math. Analysis Appl. 128 (1987), 189-204.
  • L. Schwartz, Théorie des distributions, Herman, Paris, 1966.
  • G. Talenti, Sulle equazioni integrali di Wiener-Hopf, Bollettino U.M.I. (4) 7 (1973), 18-118.
  • V.S. Vladimirov, The Wiener-Hopf equation in the Nevanlinna and Smirov algebras and ultradistributions, in Generalized functions, convergence structures, and their applications, Plenum Press, New York, 1988.
  • N. Wiener and E. Hopf, Über eine Klausse singulärer Integralgleichungen, Semester-Ber. Preuss, Akad. Wiss. Berlin, Phys.-Math, Kl., 30/32 (1931), 696-706.