Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-25T15:08:02.317Z Has data issue: false hasContentIssue false
  • English
  • Français

On an eigenfunction expansion associated with a condition of radiation

Published online by Cambridge University Press:  24 October 2008

D. Naylor
D. Naylor
Affiliation:
University of Western Ontario
Get access Rights & Permissions [Opens in a new window]

Extract

In this paper certain Bessel type eigenfunction expansions are developed by considering a non-seif-adjoint problem which involves a radiation type condition

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 67 , Issue 1 , January 1970 , pp. 107 - 121
Copyright
Copyright © Cambridge Philosophical Society 1970

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)Sears, O. B. & Titchmarsh, E. C.Some eigonfunction formulae. Quart. J. Math. Oxford 1 (1950), 165–175.CrossRefGoogle Scholar
(2)Magnus, W. and Kotin, I.The zeros of the Hankol function as a function of its order. Numer. Math. 2 (1960), 228–244.CrossRefGoogle Scholar
(3)Erdelyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.High transcendental functions, vol. 2 (McGraw-Hill, 1953).Google Scholar
(4)Watson, G. N.Theory of Bessel functions, Second Edition (Cambridge University Press, 1958).Google Scholar
(5)Naylor, D. & Dennis, S. C. R.On a singular eigenvalue problem. Proc. Cambridge Philos. Soc. 64 (1968), 439–446.CrossRefGoogle Scholar
(6)Cohen, D. S.Eigenfunction expansions and non-self adjoint boundary value problems. Comm. Pure Appl. Math. 17 (1964), 23–34.CrossRefGoogle Scholar
(7)Pflumm, E.Expansion problems arising from the Watson transformation (New York University, Division of Electromagnetic Research, Report BR 35, 1960).Google Scholar
(8)Titchmarsh, E. C.Eigenfunction expansions associated with second order differential equations, Part 1, Second edition (Oxford University Press, 1962).CrossRefGoogle Scholar
(9)Cochran, J. A.The zeros of Hankel functions as functions of their order. Numer. Math. 7 (1965), 238–250.CrossRefGoogle Scholar
(10)Keller, J. B., Rubinow, S. I. & Goldstein, M.Zeros of Hankel functions and poles of scattering amplitudes. J. Mathematical Phys. 4 (1963), 829–832.CrossRefGoogle Scholar
(11)Ursell, F.Creeping modes in a shadow. Proc. Cambridge Philos. Soc. 64 (1968), 171–191.CrossRefGoogle Scholar