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Ogden RD, Vági S. Harmonic Analysis and H-Functions on Siegel Domains of Type II. Proc Natl Acad Sci U S A. 1972;69(1):11-4doi: 10.1073/pnas.69.1.11.
Ogden, R. D., & Vági, S. (1972). Harmonic Analysis and H-Functions on Siegel Domains of Type II. Proceedings of the National Academy of Sciences of the United States of America, 69(1), 11-4. https://doi.org/10.1073/pnas.69.1.11
Ogden, R D, and Vági, S. "Harmonic Analysis and H-Functions on Siegel Domains of Type II." Proceedings of the National Academy of Sciences of the United States of America vol. 69,1 (1972): 11-4. doi: https://doi.org/10.1073/pnas.69.1.11
Ogden RD, Vági S. Harmonic Analysis and H-Functions on Siegel Domains of Type II. Proc Natl Acad Sci U S A. 1972 Jan;69(1):11-4. doi: 10.1073/pnas.69.1.11. PMID: 16591961; PMCID: PMC427533.
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Proc Natl Acad Sci U S A. 1972 Jan;69(1):11-4. doi: 10.1073/pnas.69.1.11.

Harmonic Analysis and H-Functions on Siegel Domains of Type II.

Proceedings of the National Academy of Sciences of the United States of America

R D Ogden, S Vági

Affiliations

  1. DePaul University, Chicago, Illinois 60614.

PMID: 16591961 PMCID: PMC427533 DOI: 10.1073/pnas.69.1.11

Abstract

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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