On an inversion formula
Glasgow mathematical journal, Tome 24 (1983) no. 2, pp. 149-159

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper the author considers the problem of finding a formula of inversion for the integral transform defined by the equationwhere 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:
Naylor, D. On an inversion formula. Glasgow mathematical journal, Tome 24 (1983) no. 2, pp. 149-159. doi: 10.1017/S001708950000522X
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[1] 1.Conde, S. & Kalla, S. L., The v-zeros of J(x), Math. Comp. 33 (1979), 423–426. Google Scholar

[2] 2.Magnus, W., Oberhettinger, F. & Soni, R. P., Formulas and theorems for the special functions of mathematical physics (Springer-Verlag, 1966). Google Scholar | DOI

[3] 3.Naylor, D., An eigenvalue problem in cylindrical harmonics, J. Math, and Physics 44 (1965), 391–402. Google Scholar | DOI

[4] 4.Naylor, D., On an eigenfunction expansion associated with a condition of radiation, Proc. Camb. Phil. Soc. 67 (1970), 107–121. Google Scholar | DOI

[5] 5.Naylor, D., On an integral transform occuring in the theory of diffraction, SIAM. J. Math. Anal. 8 (1977), 402–411. Google Scholar | DOI

[6] 6.Naylor, D., On an integral transform, Glasgow Math. J. 20 (1979), 1–14. Google Scholar | DOI

[7] 7.Titchmarsh, E. C., Theory of functions, 2nd ed., (Oxford University Press, 1959). Google Scholar

[8] 8.Titchmarsh, E. C., Introduction to the theory of Fourier integrals (Oxford University Press, 1950). Google Scholar

[9] 9.Watson, G. N., Theory of Bessel Functions, 2nd ed. (Cambridge University Press, 1958). Google Scholar

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