We prove admissible convergence to the boundary of functions that are harmonic on a subset of a homogeneous tree by means of a discrete Green formula and an analogue of the Lusin area function.

Atanasi, L., & Picardello, A.M. (2008). The Lusin area function and local admissible convergence of harmonic functions on homogeneous trees. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 360(6), 3327-3343 [10.1090/S0002-9947-07-04433-9].

The Lusin area function and local admissible convergence of harmonic functions on homogeneous trees

PICARDELLO, ANGELO MASSIMO
2008

Abstract

We prove admissible convergence to the boundary of functions that are harmonic on a subset of a homogeneous tree by means of a discrete Green formula and an analogue of the Lusin area function.
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - Analisi Matematica
English
boundary behavior of harmonic functions; admissible convergence; local Fatou theorem; Lusin area integral; trees
The first paper that applies differential geometric methods to solve a fundamental problem of potential theory (nontangential convergence of harmonic functions) on a discrete environment (a homogeneous tree)
Atanasi, L., & Picardello, A.M. (2008). The Lusin area function and local admissible convergence of harmonic functions on homogeneous trees. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 360(6), 3327-3343 [10.1090/S0002-9947-07-04433-9].
Atanasi, L; Picardello, Am
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/29168
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