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Remarks on a theorem of Koranyi and Malliavin on the Siegel upper half plane of rank two


Author: Kenneth D. Johnson
Journal: Proc. Amer. Math. Soc. 67 (1977), 351-356
MSC: Primary 22E30; Secondary 32M15
MathSciNet review: 0476918
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Abstract: In [5], A. Koranyi and P. Malliavin showed that bounded functions on the Siegel upper half plane of rank two which satisfied two special elliptic differential equations were characterized by their values on the Bergman-Šilov boundary. In this paper a simple proof of this theorem is given.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0476918-8
Keywords: Poisson kernel, Bergman-Šilov boundary, Furstenberg boundary, symplectic transformations
Article copyright: © Copyright 1977 American Mathematical Society