TITLE: Laplace transform on the cone of positive-definite matrices
QUESTION [7 upvotes]: The title says most. Let $P_p$ be the cone of positive-definite $p \times p$ matrices. 
One can define the Laplace transform of (the distribution of) a random matrix with values in $P_p$ by (for instance, Muirhead: "Aspects of Multivariate Analysis") the integral
\begin{equation}
     \phi(\Theta) = \int_{P_p} \exp(\sum_{j\le k}^p \theta_{jk} a_{jk}) f(A)\; dA
\end{equation}
where $f(A)$ is the density function of $A$. (And $\Theta$ is a symmetric $p\times p$-matrix)
So the question is: I am searching for references for this Laplace transform, inversion theorems, numerical methods, known transform formulas, .... etc ???
Thanks for answers!  Now, I am searching for those references, but one is really difficult to find, that is, volume 2 of Audrey Terras' book: "Harmonic analysis on symmetric spaces II"
I have found the first volume, but volume II cannot even be found on Springers own website!  Any ideas about how to find it?

REPLY [4 votes]: Second editions of both volumes are about to be published.
It will probably take a year to update them though.
              audrey