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Matrices Associated with Fractional Hankel and Fourier Transformations

Published online by Cambridge University Press:  18 May 2009

A. P. Guinand
A. P. Guinand
Affiliation:
University of New England, Armidale, N.S.W., Australia
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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(2x½).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 2 , Issue 4 , February 1956 , pp. 185 - 192
Copyright
Copyright © Glasgow Mathematical Journal Trust 1956

References

REFERENCES

(1)Barrucand, P., Sur les suites réciproques, Comptes Rendus, 230 (1950), 1727–8.Google Scholar
(2)Cooke, R. G., Infinite matrices and sequence spaces (London, 1950), 20.Google Scholar
(3)Kober, H., Wurzeln avis der Hankel-, Fourier-, und aus anderen stetigen Transformationen, Quart. J. Math. (Oxford), (1) 10 (1939), 45–59.CrossRefGoogle Scholar
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