The Hua system on irreducible Hermitian symmetric spaces of nontube type

Dariusz Buraczewski[1]

  • [1] Uniwersytet Wroclawski, Instytut Matematyczny, Plac Grunwaldzki 2/4, 50-384 Wroclaw, (Pologne)

Annales de l’institut Fourier (2004)

  • Volume: 54, Issue: 1, page 81-127
  • ISSN: 0373-0956

Abstract

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Let G / K be an irreducible Hermitian symmetric space of noncompact type. We study a G - invariant system of differential operators on G / K called the Hua system. It was proved by K. Johnson and A. Korányi that if G / K is a Hermitian symmetric space of tube type, then the space of Poisson-Szegö integrals is precisely the space of zeros of the Hua system. N. Berline and M. Vergne raised the question about the nature of the common solutions of the Hua system for Hermitian symmetric spaces of nontube type. In this paper we show that these are exactly the pluriharmonic functions.

How to cite

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Buraczewski, Dariusz. "The Hua system on irreducible Hermitian symmetric spaces of nontube type." Annales de l’institut Fourier 54.1 (2004): 81-127. <http://eudml.org/doc/116109>.

@article{Buraczewski2004,
abstract = {Let $G/K$ be an irreducible Hermitian symmetric space of noncompact type. We study a $G$- invariant system of differential operators on $G/K$ called the Hua system. It was proved by K. Johnson and A. Korányi that if $G/K$ is a Hermitian symmetric space of tube type, then the space of Poisson-Szegö integrals is precisely the space of zeros of the Hua system. N. Berline and M. Vergne raised the question about the nature of the common solutions of the Hua system for Hermitian symmetric spaces of nontube type. In this paper we show that these are exactly the pluriharmonic functions.},
affiliation = {Uniwersytet Wroclawski, Instytut Matematyczny, Plac Grunwaldzki 2/4, 50-384 Wroclaw, (Pologne)},
author = {Buraczewski, Dariusz},
journal = {Annales de l’institut Fourier},
keywords = {pluriharmonic functions; Hua system; Hermitian symmetric spaces; Siegel domains},
language = {eng},
number = {1},
pages = {81-127},
publisher = {Association des Annales de l'Institut Fourier},
title = {The Hua system on irreducible Hermitian symmetric spaces of nontube type},
url = {http://eudml.org/doc/116109},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Buraczewski, Dariusz
TI - The Hua system on irreducible Hermitian symmetric spaces of nontube type
JO - Annales de l’institut Fourier
PY - 2004
PB - Association des Annales de l'Institut Fourier
VL - 54
IS - 1
SP - 81
EP - 127
AB - Let $G/K$ be an irreducible Hermitian symmetric space of noncompact type. We study a $G$- invariant system of differential operators on $G/K$ called the Hua system. It was proved by K. Johnson and A. Korányi that if $G/K$ is a Hermitian symmetric space of tube type, then the space of Poisson-Szegö integrals is precisely the space of zeros of the Hua system. N. Berline and M. Vergne raised the question about the nature of the common solutions of the Hua system for Hermitian symmetric spaces of nontube type. In this paper we show that these are exactly the pluriharmonic functions.
LA - eng
KW - pluriharmonic functions; Hua system; Hermitian symmetric spaces; Siegel domains
UR - http://eudml.org/doc/116109
ER -

References

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