Let ∆ be a thick affine building of type ~ A_2. We prove that each positive harmonic function on ∆ is the Poisson transform of a positive measure on the maximal boundary Ω. Moreover we prove that if f is weakly harmonic and bounded, then f is harmonic.
Remarks on harmonic functions on affine buildings
MANTERO, ANNA MARIA;ZAPPA, ANNA
2004-01-01
Abstract
Let ∆ be a thick affine building of type ~ A_2. We prove that each positive harmonic function on ∆ is the Poisson transform of a positive measure on the maximal boundary Ω. Moreover we prove that if f is weakly harmonic and bounded, then f is harmonic.
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