Geodesic
Matrices Associated with Fractional Hankel and Fourier Transformations
Glasgow mathematical journal, Tome 2 (1956) no. 4, pp. 185-192

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

Several writers (4), (6), (7), (9) have used orthogonal expansions in discussing properties of Fourier transformations, and Kober (3) has used such expansions to derive fractional Fourier and Hankel transformations. In 1950 Barrucand (1) noted a reciprocity holding between the coefficients in the expansions in Laguerre polynomials of pairs of functions which are transforms with respect to the kernel J0(2x1⁄2). 
Guinand, A. P. Matrices Associated with Fractional Hankel and Fourier Transformations. Glasgow mathematical journal, Tome 2 (1956) no. 4, pp. 185-192. doi: 10.1017/S2040618500033323
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[(1)] (1)Barrucand, P., Sur les suites réciproques, Comptes Rendus, 230 (1950), 1727–8. Google Scholar

[(2)] (2)Cooke, R. G., Infinite matrices and sequence spaces (London, 1950), 20. Google Scholar

[(3)] (3)Kober, H., Wurzeln avis der Hankel-, Fourier-, und aus anderen stetigen Transformationen, Quart. J. Math. (Oxford), (1) 10 (1939), 45–59. Google Scholar | DOI

[(4)] (4)Plancherel, M., Contribution à l'étude de la représentation d'une fonction arbitraire par des intégrales définies, Rend, di Palermo, 30 (1910), 289–335. Google Scholar | DOI

[(5)] (5)Szegö, G., Orthogonal polynomials, American. Math. Soc. Colloquium Publications, Vol. XXIII (1939). Google Scholar

[(6)] (6)Titchmarsh, E. C., Hankel transforms, Proc. Cambridge Phil. Soc., 21 (1923), 463–73. Google Scholar

[(7)] (7)Titchmarsh, E. C., Introduction to the theory of Fourier integrals (2nd edition, Oxford, 1948), 76–83. Google Scholar

[(8)] (8)Watson, G. N., A treatise on the theory of Bessel functions (2nd edition, Cambridge, 1941), 394 (4). Google Scholar

[(9)] (9)Wiener, N., The Fourier integral (Cambridge, 1922), Chapter I. Google Scholar

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