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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A nonlinear boundary problem

Author: John R. Hatcher
Journal: Proc. Amer. Math. Soc. 95 (1985), 441-448
MSC: Primary 30E25; Secondary 45E10
MathSciNet review: 806084
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Abstract: A nonlinear Hilbert problem of power type is solved in closed form by representing a sectionally holomorphic function by means of an integral with power kernel. This technique transforms the problem to one of solving an integral equation of the generalized Abel type.

References [Enhancements On Off] (What's this?)

  • K. D. Sakalyuk, Abel’s generalized integral equation, Soviet Math. Dokl. 1 (1960), 332–335. MR 0117520
  • N. I. Muskhelishvili, Singular integral equations, Wolters-Noordhoff Publishing, Groningen, 1972. Boundary problems of functions theory and their applications to mathematical physics; Revised translation from the Russian, edited by J. R. M. Radok; Reprinted. MR 0355494
  • Norman Levinson, Simplified treatment of integrals of Cauchy type, the Hilbert problem and singular integral equations. Appendix: Poincaré-Bertrand formula, SIAM Rev. 7 (1965), 474–502. MR 185398, DOI
  • Wilhelm Magnus, Fritz Oberhettinger, and Raj Pal Soni, Formulas and theorems for the special functions of mathematical physics, Third enlarged edition, Die Grundlehren der mathematischen Wissenschaften, Band 52, Springer-Verlag New York, Inc., New York, 1966. MR 0232968

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Keywords: Cauchy integral, Plemelj formulae, nonhomogeneous boundary value problem
Article copyright: © Copyright 1985 American Mathematical Society