Harmonic Analysis and H2-Functions on Siegel Domains of Type II

摘要

It is known that the distinguished boundary of a Siegel domain of type II can be identified with a simply connected nilpotent Lie group of step two. The Plancherel formula for this group and the irreducible unitary representations which enter into that formula are determined. The H²-space of the domain and its Szegö kernel are characterized in terms of the harmonic analysis of the above group, in particular, the integral representations for H²-functions due to Gindikin and Korányi-Stein are shown to be instances of the Fourier inversion formula.