Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-25T01:09:31.049Z Has data issue: false hasContentIssue false

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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