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1. CJM 1999 (vol 51 pp. 816)

Hall, Brian C.
A New Form of the Segal-Bargmann Transform for Lie Groups of Compact Type
I consider a two-parameter family $B_{s,t}$ of unitary transforms mapping an $L^{2}$-space over a Lie group of compact type onto a holomorphic $L^{2}$-space over the complexified group. These were studied using infinite-dimensional analysis in joint work with B.~Driver, but are treated here by finite-dimensional means. These transforms interpolate between two previously known transforms, and all should be thought of as generalizations of the classical Segal-Bargmann transform. I consider also the limiting cases $s \rightarrow \infty$ and $s \rightarrow t/2$.

Categories:22E30, 81S30, 58G11

2. CJM 1997 (vol 49 pp. 359)

Sawyer, P.
Estimates for the heat kernel on $\SL (n,{\bf R})/\SO (n)$
In \cite{Anker}, Jean-Philippe Anker conjectures an upper bound for the heat kernel of a symmetric space of noncompact type. We show in this paper that his prediction is verified for the space of positive definite $n\times n$ real matrices.

Categories:58G30, 53C35, 58G11

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