Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-28T02:02:34.584Z Has data issue: false hasContentIssue false
  • English
  • Français

A class of integral equations

Published online by Cambridge University Press:  24 October 2008

W. E. Williams
W. E. Williams
Affiliation:
Applied Mathematics Department, Liverpool University
Get access Rights & Permissions [Opens in a new window]

Extract

It was pointed out by Copson(1) in 1947 that the solution of the integral equation for the electrostatic problem for a circular disc could be reduced to the solution of Abel integral equations and hence a solution obtained in a fairly elementary manner. This result was obtained independently by Lebedev(2), who also obtained a similar result for the electrostatic problem for the spherical cap. The solution for the spherical cap was also obtained independently by Collins (3). In view of the relative simplicity of the approach it seems to be of interest to examine whether there exist other integral equations which can be treated in a similar fashion. In the present paper one such class of integral equations will be considered.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 3 , July 1963 , pp. 589 - 597
Copyright
Copyright © Cambridge Philosophical Society 1963

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)Copson, E. T.Proc. Edinburgh Math. Soc. 8 (1947), 14.CrossRefGoogle Scholar
(2)Lebedev, N. N.Z. Tehn. Fiz. 18 (1948), 773.Google Scholar
(3)Collins, W. D.Proc. Cambridge Philos. Soc. 55 (1959), 377.CrossRefGoogle Scholar
(4)Mossakovskii, V. I.Prikl. Mat. Meh. 22 (1958), 168.Google Scholar
(5)Popov, G. I.Prikl. Mat. Meh. 25 (1961), 105.Google Scholar
(6)Rostovtsev, N. A.Prikl. Mat. Meh. 25 (1961), 238.Google Scholar
(7)Lewin, L. Advanced theory of wave guides, ch. 3 (Iliffe; London, 1951).Google Scholar
(8)Carleman, T.Math. Z. 15 (1922), 111.Google Scholar
(9)Jones, D. S.Comm. Pure Appl. Math. 9 (1956), 713.CrossRefGoogle Scholar
(10)Williams, W. E.Proc. Roy. Soc. London, Ser. A, 267 (1962), 77.Google Scholar
(11)Watson, G. N.Theory of Bessel functions. 2nd ed. (Cambridge University Press, 1944).Google Scholar
(12)Ebdéelyi, A. et al. Higher transcendental functions, vol. I (McGraw-Hill; New York, 1954).Google Scholar
(13)Noble, B.Proc. Cambridge Philos. Soc. 59 (1963), 363.CrossRefGoogle Scholar
(14)Latta, G.Applied Maths. Report No. 32 (Stanford University, 1955).Google Scholar
(15)Tranter, C.J. Proc. Glasgow Math. Assoc. 4 (1959), 49.CrossRefGoogle Scholar
(16)Muskhelishvili, N. I.Singular integral equations (Noordhoff; Groningen, 1953).Google Scholar
(17)Tricomi, F.Integral equations (Interscience; New York, 1957).Google Scholar
(18)Noble, B.Math. Phys. 37 (1958), 128.CrossRefGoogle Scholar
(19)Noble, B.Proc. Cambridge Philos. Soc. 59 (1963), 351.CrossRefGoogle Scholar
(20)Williams, W. E.Proc. Edinburgh Math. Soc. 12 (1961), 213.CrossRefGoogle Scholar
(21)Collins, W. D.Proc. Cambridge Philos. Soc. 57 (1961), 367.CrossRefGoogle Scholar