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Solution of hypergeometric integral equations involving generalised functions

Published online by Cambridge University Press:  20 January 2009

Adam C. McBride
Adam C. McBride
Affiliation:
Department of Mathematics, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow, Gl 1XH
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In a previous paper (9), we introduced the spaces Fp, μ of testing-functions and the corresponding spaces of generalised functions. For 1≦p≦∞, Fp(=Fp, 0) is the linear space of all complex-valued measurable functions φ defined on (0, ∞) which are infinitely differentiable on (0, ∞) and for which

for each k = 0, 1, 2, …. In symbols,

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 19 , Issue 3 , March 1975 , pp. 265 - 285
Copyright
Copyright © Edinburgh Mathematical Society 1975

References

REFERENCES

(1) Erdelyi, A., Fractional integrals of generalised functions, J. Austral. Math. Soc. 14 (1972), 30–37.CrossRefGoogle Scholar
(2) Erdelyi, A. et al. , Higher Transcendental Functions, Vol. I (McGraw-Hill, New York, 1953).Google Scholar
(3) Higgins, T. P., A hypergeometric function transform, J. Soc. Indust. Appl.Math. 12 (1964), 601–612.CrossRefGoogle Scholar
(4) Kober, H., On fractional integrals and derivatives, Quart. J. Math. (Oxford) 11 (1940), 193–211.CrossRefGoogle Scholar
(5) Love, E. R., Some integral equations involving hypergeometric functions, Proc. Edinburgh Math. Soc. (2) 15 (1967), 169–198.CrossRefGoogle Scholar
(6) Love, E. R., TWO more hypergeometric integral equations, Proc. Cambridge Philos. Soc. 63 (1967), 1055–1076.CrossRefGoogle Scholar
(7) Love, E. R., Two index laws for fractional integrals and derivatives, J. Austral. Math. Soc. 14 (1972), 385–410.CrossRefGoogle Scholar
(8) Mcbride, A. C., A Theory of Fractional Integration for Generalised Functions with Applications, Ph.D. Thesis, University of Edinburgh (1971).Google Scholar
(9) McBride, A. C., A theory of fractional integration for generalised functions, SIAM J. Math. Anal. (to appear).Google Scholar
(10) Zemanian, A. H., Generalised Integral Transformations (Interscience, New York, 1968).Google Scholar