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On integral operators with kernels involving Bessel functions

Published online by Cambridge University Press:  24 October 2008

G. O. Okikiolu
G. O. Okikiolu
Affiliation:
University of East Anglia
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Abstract

By representing integral operators defined by kernels involving Bessel functions as compositions of two operators, we determine their mapping properties and, in one case, derive an inversion process. The operators considered are of the form

where τ(t) is given respectively by and and in the last three cases the integrals converge in norm.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 3 , July 1966 , pp. 477 - 484
Copyright
Copyright © Cambridge Philosophical Society 1966

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References

REFERENCES

(1)Fox, C.An inversion formula for the kernel K ν(x). Proc. Cambridge Philos. Soc 61 (1965), 457–467.CrossRefGoogle Scholar
(2)Hardy, G. H., Littlewood, J. E. and Polya, G.Inequalities (Cambridge, 1934).Google Scholar
(3)Kober, H.On fractional integrals and derivatives. Quart. J. Math. Oxford 11 (1940), 193–211.CrossRefGoogle Scholar
(4)Okikiolu, G. O.On certain bounded linear operators in L spaces. J. London Math. Soc. (to appear).Google Scholar
(5)Titchmarsh, E. C.The theory of Fourier integrals, 2nd edition (Oxford, 1948).Google Scholar