Wavelet transform associated to a homogeneous Siegel domain

摘要

Let D be a homogeneous Siegel domain of non-tube type and G a completely solvable Lie group acting on D simply transitively as affine transformations. After giving an irreducible decomposition of the unitary representation of G defined on the L~2-function space over the Shilov boundary of D, we consider the continuous wavelet transform associated to each irreducible subrepresentation.