International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 3, Pages 503-511

Generalized Laplace transform with matrix variables

R. M. Joshi and J. M. C. Joshi

Department of Mathematics, Govt. P. G. College, Pithoragarh, (U.P.), India

Received 9 September 1985

Copyright © 1987 R. M. Joshi and J. M. C. Joshi. 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.


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()d

The 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.