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On an inversion formula

Published online by Cambridge University Press:  18 May 2009

D. Naylor
D. Naylor
Affiliation:
University of Western Ontario London, Ontario Canada
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In this paper the author considers the problem of finding a formula of inversion for the integral transform defined by the equation

where a >0, k > 0 and r-1f(r) εL (a, ∞). This transform appeared in connection with an earlier investigation [4] in which an attempt was made to devise an integral transform that could be adapted to the solution of certain boundary value problems involving the space form of the wave equation and the condition of radiation:

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 24 , Issue 2 , July 1983 , pp. 149 - 159
Copyright
Copyright © Glasgow Mathematical Journal Trust 1983

References

REFERENCES

1.Conde, S. & Kalla, S. L., The v-zeros of J-v(x), Math. Comp. 33 (1979), 423–426.Google Scholar
2.Magnus, W., Oberhettinger, F. & Soni, R. P., Formulas and theorems for the special functions of mathematical physics (Springer-Verlag, 1966).CrossRefGoogle Scholar
3.Naylor, D., An eigenvalue problem in cylindrical harmonics, J. Math, and Physics 44 (1965), 391–402.CrossRefGoogle Scholar
4.Naylor, D., On an eigenfunction expansion associated with a condition of radiation, Proc. Camb. Phil. Soc. 67 (1970), 107–121.CrossRefGoogle Scholar
5.Naylor, D., On an integral transform occuring in the theory of diffraction, SIAM. J. Math. Anal. 8 (1977), 402–411.CrossRefGoogle Scholar
6.Naylor, D., On an integral transform, Glasgow Math. J. 20 (1979), 1–14.CrossRefGoogle Scholar
7.Titchmarsh, E. C., Theory of functions, 2nd ed., (Oxford University Press, 1959).Google Scholar
8.Titchmarsh, E. C., Introduction to the theory of Fourier integrals (Oxford University Press, 1950).Google Scholar
9.Watson, G. N., Theory of Bessel Functions, 2nd ed. (Cambridge University Press, 1958).Google Scholar