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On fractional integration of generalized functions on a half-line

Published online by Cambridge University Press:  20 January 2009

B. Rubin
B. Rubin
Affiliation:
Department of Mathematics, The Hebrew University of Jerusalem, Givat Ram 91904, Jerusalem, Israel Email: [email protected]
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Abstract

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A new approach to fractional integrals of distributions on a half-line is suggested. The results admit an extension to a large class of Mellin convolutions.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 38 , Issue 3 , October 1995 , pp. 387 - 396
Copyright
Copyright © Edinburgh Mathematical Society 1995

References

REFERENCES

1.Mcbride, A. C., Fractional calculus and integral transforms of generalized functions (Research Notes in Math. 31, Pitman, London, 1979).Google Scholar
2.Mcbride, A. C., A Mellin transform approach to fractional calculus on (0, ∞), in Fractional Calculus (Research Notes in Math. 138, Pitman, London, 1985), 99–139.Google Scholar
3.Erdélyi, A., Fractional integrals of generalized functions, Lecture Notes in Math. 457 (1975), 151–170.CrossRefGoogle Scholar
4.Brychkov, Y. A., Prudnikov, A. P., Integral transforms of generalized functions (Moscow, 1977 (in Russian)).Google Scholar
5.Lizorkin, P. I., Generalized Liouville differentiation and the method of multipliers in the theory of imbeddings of classes of differentiable functions, Proc. Steklov. Inst. Math. 105 (1969), 105–202.Google Scholar
6.Brychkov, Y. A., Glaeske, H.-J. and Marichev, O. I., The factorization of integral transforms of the convolution type, Itogi Nauki i Tekhniki., VINITI, Math. Anal. 21 (1983), 3–41.Google Scholar
7.Gradshteyn, I. S. and Ryzhik, I. M., Table of Integrals, Series and Products Academic Press 1980.Google Scholar
8.Samko, S. G., Hypersingular integrals and their applications (Rostov-on-Don, 1984 (in Russian).Google Scholar