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(∧)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.