Author’s abstract: “Let

$\mathbf{D}=G/K$ be a complex bounded symmetric domain of tube type in a Jordan algebra

${V}_{C}$ and let

$D=H/L=\mathbf{D}\cap V$ be its real form in a Jordan algebra

$V\subset {V}_{C}$. The analytic continuation of the holomorphic discrete series on

$\mathbf{D}$ forms a family of interesting representations of

$G$. We consider the restriction on

$D$ and the branching rule under

$H$ of the scalar holomorphic representations. The unitary part of the restriction map gives then a generalization of the Segal-Bargmann transform. The group

$L$ is a spherical subgroup of

$K$ and we find a canonical basis of

$L$-invariant polynomials in the components of the Schmid decomposition and we express them in terms of the Jack symmetric polynomials. We prove that the Segal-Bargmann transforms of those

$L$-invariant polynomials are, under the spherical transform on

$D$, multi-variable Wilson-type polynomials and we give a simple alternative proof of their orthogonality relation. We find the expansion of the spherical functions on

$D$, when extended to a holomorphic function in a neighborhood of

$0\in \mathbf{D}$, in terms of the

$L$-spherical holomorphic polynomials on

$\mathbf{D}$, the coefficients being the Wilson polynomials”.