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Harmonic functions on buildings of reductive split groups. (English) Zbl 0536.22018
Operator algebras and group representations, Proc. int. Conf., Neptun/Rom. 1980, Vol. I. Monogr. Stud. Math. 17, 208-221 (1984).
[For the entire collection see Zbl 0515.00017.]
Let G be a connected reductive split group of adjoint type over p-adic field. After constructing the building \(X=X(G)\) (following Bruhat-Tits), the author introduces a compactification of X analogous to the Satake compactification of a symmetric space, then he defines harmonic functions and shows, in certain cases, that they are defined by their boundary values on the distinguished boundary.
Reviewer: F.Rouvière

22E35 Analysis on \(p\)-adic Lie groups
43A85 Harmonic analysis on homogeneous spaces
31B25 Boundary behavior of harmonic functions in higher dimensions