Local admissible convergence of harmonic functions on non-homogeneous trees

• Autorzy: Massimo A. Picardello
• Języki publikacji: EN

Abstrakty

EN

We prove admissible convergence to the boundary of functions that are harmonic on a subset of a non-homogeneous tree equipped with a transition operator that satisfies uniform bounds suitable for transience. The approach is based on a discrete Green formula, suitable estimates for the Green and Poisson kernel and an analogue of the Lusin area function.

Kategorie tematyczne

• 05C05: Trees
• 60J45: Probabilistic potential theory
• 31A20: Boundary behavior (theorems of Fatou type, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 118
• Numer: 2
• Strony: 419-444

Daty

wydano

2010

Twórcy

autor

Massimo A. Picardello

• Dipartimento di Matematica, Università di Roma "Tor Vergata", Via della Ricerca Scientifica, 00133 Roma, Italy

Identyfikatory

DOI

10.4064/cm118-2-5