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On some Cauchy-separable integral equations

Published online by Cambridge University Press:  24 October 2008

D. Porter
Affiliation:
Department of Mathematics, University of Reading, Reading RG6 2AX

Extract

In a recent paper, Porter [9] devised two generalized Volterra operators which convert integral equations with the Hankel function kernel into Cauchy singular equations. The transformations were exploited in [9], and in a subsequent paper (Porter and Chu [10]), in relation to certain wave diffraction problems.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

REFERENCES

[1]Abramowitz, M. and Stegun, I. A.. Handbook of Mathematical Functions (Dover, 1972).Google Scholar
[2]Gradsteyn, I. S. and Ryzhik, I. M.. Tables of Integrals, Series and Products (Academic Press, 1981).Google Scholar
[3]Hochstadt, H.. Integral Equations (Wiley-Interscience, 1973).Google Scholar
[4]Jones, D. S.. On a certain singular integral equation I. J. Math. Phys. 43 (1964), 2733.CrossRefGoogle Scholar
[5]Jones, D. S.. On a certain singular integral equation. II. J. Math. Phys. 43 (1964), 263273.CrossRefGoogle Scholar
[6]Jones, D. S.. Diffraction at high frequencies by a circular disc. Proc. Cambridge Philos. Soc. 61 (1965), 223245.CrossRefGoogle Scholar
[7]Noble, B.. The Wiener-Hopf Technique (Pergamon Press, 1958).Google Scholar
[8]Peters, A. S.. Some integral equations related to Abel’s equation and the Hilbert transform. Comm. Pure Appl. Math. 22 (1969), 539560.CrossRefGoogle Scholar
[9]Porter, D.. On some integral equations with a Hankel function kernel. IMA J. Appl. Math. 33 (1984), 211228.CrossRefGoogle Scholar
[10]Porter, D. and Chu, K. W. E.. The solution of two wave diffraction problems. J. Engineering Math. (to appear).Google Scholar
[11]Porter, D.. The reduction of a pair of singular integral equations. Math. Proc. Cambridge Philos. Soc. 100 (1986) (to appear).CrossRefGoogle Scholar
[12]Sewell, M. J.. Maximum and Minimum Principles (Cambridge University Press, 1986).Google Scholar
[13]Spence, D. A.. A Wiener-Hopf equation arising in elastic contact problems. Proc. Roy. Soc. London A 305 (1968), 8192.Google Scholar