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Remarks on a theorem of Koranyi and Malliavin on the Siegel upper half plane of rank two. (English) Zbl 0395.22012


MSC:

22E30 Analysis on real and complex Lie groups
32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)
43A85 Harmonic analysis on homogeneous spaces
53C35 Differential geometry of symmetric spaces

Citations:

Zbl 0318.60066
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References:

[1] Harry Furstenberg, A Poisson formula for semi-simple Lie groups, Ann. of Math. (2) 77 (1963), 335 – 386. · Zbl 0192.12704 · doi:10.2307/1970220
[2] L. K. Hua, Harmonic analysis of functions of several complex variables in the classical domains, Translated from the Russian by Leo Ebner and Adam Korányi, American Mathematical Society, Providence, R.I., 1963.
[3] S. Helgason and A. Korányi, A Fatou-type theorem for harmonic functions on symmetric spaces, Bull. Amer. Math. Soc. 74 (1968), 258 – 263. · Zbl 0153.42902
[4] Kenneth D. Johnson, Differential equations and the Bergman-Šilov boundary on the Siegel upper half plane, Ark. Mat. 16 (1978), no. 1, 95 – 108. · Zbl 0395.22013 · doi:10.1007/BF02385985
[5] A. Korányi and P. Malliavin, Poisson formula and compound diffusion associated to an overdetermined elliptic system on the Siegel halfplane of rank two, Acta Math. 134 (1975), no. 3-4, 185 – 209. · Zbl 0318.60066 · doi:10.1007/BF02392101
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