Open AccessHarmonic Analysis and H 2 -Functions on Siegel Domains of Type II
Author(s) -
Robert D. Ogden,
Stephen Vági
Publication year - 1972
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.69.1.11
Subject(s) - mathematics , pure mathematics , lie group , group (periodic table) , type (biology) , simply connected space , kernel (algebra) , nilpotent , domain (mathematical analysis) , harmonic function , fourier transform , boundary (topology) , unitary state , mathematical analysis , algebra over a field , physics , quantum mechanics , ecology , political science , law , biology
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.