We study a natural system of second order differential operators on a symmetric Siegel domain that is invariant under the action of biholomorphic transformations. If is of type two, the space of real valued solutions coincides with pluriharmonic functions. We show the main idea of the proof and give a survey of previous results.
@article{RLIN_2002_9_13_3-4_199_0,
author = {Dariusz Buraczewski and Ewa Damek},
title = {Hua-harmonic functions on symmetric type two Siegel domains},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
volume = {13},
year = {2002},
pages = {199-207},
zbl = {1225.32004},
mrnumber = {1984100},
language = {en},
url = {http://dml.mathdoc.fr/item/RLIN_2002_9_13_3-4_199_0}
}
Buraczewski, Dariusz; Damek, Ewa. Hua-harmonic functions on symmetric type two Siegel domains. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 13 (2002) pp. 199-207. http://gdmltest.u-ga.fr/item/RLIN_2002_9_13_3-4_199_0/
[1] - , Equations de Hua et noyau de Poisson. Lecture Notes in Mathematics, vol. 880, Springer-Verlag, 1981, 1-51. | MR 644825 | Zbl 0521.32024
[2] - - - - - , Hua system and pluriharmonicity for symmetric irreducible Siegel domains of type II. Journal of Functional Analysis, 188, n. 1, 2002, 38-74. | MR 1878631 | Zbl 0999.31005
[3] , Pluriharmonicity of Hua harmonic functions on symmetric irreducible Siegel domains of type II. Preprint.
[4] - - , Bounded plurihramonic functions on symmetric irreducible Siegel domains. Mathematische Zeitschrift, to appear. | MR 1906712 | Zbl 1008.32013
[5] - , Pluriharmonic functions on symmetric irreducible Siegel domains. Studia Math., 139, n. 2, 2000, 104-140. | MR 1762449 | Zbl 0999.32012
[6] - - - , Pluriharmonic functions on symmetric irreducible Siegel domains. Geom. and Funct. Analysis, 10, 2000, 1090-1117. | MR 1792830 | Zbl 0969.31007
[7] , Discrete series for semisimple Lie groups II. Acta Math., 116, 1960, 1-111. | Zbl 0199.20102
[8] , Geometric Analysis on Symmetric Spaces. Amer. Math. Soc., Providence1994. | MR 1280714 | Zbl 1157.43003
[9] , Harmonic Analysis of Functions of Several Complex Variables in Classical Domains. Translations of Math. Monographs, vol. 6, Amer. Math. Soc., Providence1963. | MR 171936 | Zbl 0112.07402
[10] , Remarks on the theorem of Korányi and Malliavin on the Siegel upper half-plane of rank two. Proc. Amer. Math. Soc., 67, 1977, 351-356. | MR 476918 | Zbl 0395.22012
[11] , Differential equations and the Bergman-Shilov boundary on the Siegel upper half-plane. Arkiv for Matematik, 16, 1978, 95-108. | MR 499140 | Zbl 0395.22013
[12] - , The Hua operators on bounded symmetric domains of tube type. Ann. of Math., (2) 111, n. 3, 1980, 589-608. | MR 577139 | Zbl 0468.32007
[13] - , Poisson formula and compound diffusion associated to an overdetermined elliptic system on the Siegel halfplane of rank two. Acta Math., 134, 1975, 185-209. | MR 410278 | Zbl 0318.60066
[14] , Les équations de Hua d’un domaine borné symétrique du type tube. Invent. Math., 77, 1984, 129-161. | MR 751135 | Zbl 0582.32042
[15] , Geometry and classification of homogeneous bounded domains in . Uspehi Math. Nauk, 2, 1965, 3-51; Russian Math. Surv., 20, 1966, 1-48. | Zbl 0142.05002