Advanced Studies in Pure Mathematics

Cayley Transforms and Symmetry Conditions for Homogeneous Siegel Domains

Takaaki Nomura

Full-text: Open access

Abstract

In this article we first present a family of Cayley transforms of a homogeneous Siegel domain. We then give characterizations of symmetric Siegel domains among homogeneous Siegel domains in terms of norm equalities involving the Cayley transforms. Applications of these characterizations to analysis on Siegel domains (the Berezin transforms and the Poisson kernel) are also exhibited.

Article information

Source
Lie Groups, Geometric Structures and Differential Equations — One Hundred Years after Sophus Lie, T. Morimoto, H. Sato and K. Yamaguchi, eds. (Tokyo: Mathematical Society of Japan, 2002), 253-265

Dates
Received: 6 October 2000
Revised: 3 July 2001
First available in Project Euclid: 1 January 2019

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1546368696

Digital Object Identifier
doi:10.2969/aspm/03710253

Mathematical Reviews number (MathSciNet)
MR1980904

Zentralblatt MATH identifier
1035.32015

Citation

Nomura, Takaaki. Cayley Transforms and Symmetry Conditions for Homogeneous Siegel Domains. Lie Groups, Geometric Structures and Differential Equations — One Hundred Years after Sophus Lie, 253--265, Mathematical Society of Japan, Tokyo, Japan, 2002. doi:10.2969/aspm/03710253. https://projecteuclid.org/euclid.aspm/1546368696


Export citation