Harmonic Analysis and H-Functions on Siegel Domains of Type II.
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 H(2)-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 H(2)-functions due to Gindikin and Korányi-Stein are shown to be instances of the Fourier inversion formula.
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DePaul University, Chicago, Illinois 60614.
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