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On an eigenfunction expansion associated with a condition of radiation. II

Published online by Cambridge University Press:  24 October 2008

D. Naylor ,
F. C. Choo  and
D. W. Barclay
D. Naylor
Affiliation:
University of Western Ontario, London 72, Canada
F. C. Choo
Affiliation:
University of Western Ontario, London 72, Canada
D. W. Barclay
Affiliation:
University of Western Ontario, London 72, Canada
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Extract

In this paper the authors consider a problem, frequently encountered in diffraction theory, of expanding a given function f(r) in terms of a set of orthogonal functions which is not complete. The expansion in question can be written as

where r < a and

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 74 , Issue 3 , November 1973 , pp. 485 - 496
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

REFERENCES

(1)Naylor, D.On an eigenfunction expansion associated with a condition of radiation. Proc Cambridge Philos. Soc. 67 (1970), 107–121.Google Scholar
(2)Naylor, D.On an integral transform associated with a condition of radiation. Proc. Cambridge Philos. Soc. 71 (1972), 369–379.Google Scholar
(3)Pflumm, E.Expansion problems arising from the Watson transformation. New York University, Division of Electromagnetic Research, Report BR 35, 1960.Google Scholar
(4)Cohen, D. S.Eigenfunction expansions and non-self adjoint boundary value problems. Comm. Pure Appl. Math. 17 (1964), 23–34.Google Scholar
(5)Magnus, W. and Kotin, I.The zeros of the Hankel function as a function of its order. Numer. Math. 2 (1960), 228–244.Google Scholar