International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1987 / Article

Open Access

Volume 10 |Article ID 586307 | https://doi.org/10.1155/S0161171287000590

R. M. Joshi, J. M. C. Joshi, "Generalized Laplace transform with matrix variables", International Journal of Mathematics and Mathematical Sciences, vol. 10, Article ID 586307, 9 pages, 1987. https://doi.org/10.1155/S0161171287000590

Generalized Laplace transform with matrix variables

Received09 Sep 1985

Abstract

In the present paper we have extended generalized Laplace transforms of Joshi to the space of m×m symmetric matrices using the confluent hypergeometric function of matrix argument defined by Herz as kernel. Our extension is given by g(z)=Γm(α)Γm(β)>01F1(α:β:z) f()dThe convergence of this integral under various conditions has also been discussed. The real and complex inversion theorems for the transform have been proved and it has also been established that Hankel transform of functions of matrix argument are limiting cases of the generalized Laplace transforms.

Copyright © 1987 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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