Geometric norm equality related to the harmonicity of the Poisson kernel for homogeneous Siegel domains

Takaaki Nomura

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

In this paper, we present a geometric norm equality involving an admissible linear form ω for the Shilov boundary of a homogenous Siegel domain D. We prove that the validity of this norm equality is equivalent to the symmetry of D and the reduction of ω essentially to the Koszul form. This, in particular, reveals a geometric reason that the Poisson kernel is annihilated by the Laplace-Beltrami operator if and only if D is symmetric, a theorem due to Hua, Look, Korányi and Xu.

Original languageEnglish
Pages (from-to)229-267
Number of pages39
JournalJournal of Functional Analysis
Volume198
Issue number1
DOIs
Publication statusPublished - Feb 20 2003
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis

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