We consider an infinite locally finite tree $T$ equipped with nearest neighbor transition coefficients, giving rise to a space of harmonic functions. We show that, except for trivial cases, the generic harmonic function on $T$ has dense range in the complex numbers. By looking at forward-only transition coefficients, we show that the generic harmonic function induces a boundary martingale that approximates in probability all measurable functions on the boundary of $T$. We also study algebraic genericity, spaceability and frequent universality of these phenomena.

Abakumov, E., Nestoridis, V., Picardello, A.m. (2017). Universal properties of harmonic functions on trees. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 445(2), 1181-1187 [10.1016/j.jmaa.2016.03.078].

Universal properties of harmonic functions on trees

PICARDELLO, ANGELO MASSIMO
2017-01-01

Abstract

We consider an infinite locally finite tree $T$ equipped with nearest neighbor transition coefficients, giving rise to a space of harmonic functions. We show that, except for trivial cases, the generic harmonic function on $T$ has dense range in the complex numbers. By looking at forward-only transition coefficients, we show that the generic harmonic function induces a boundary martingale that approximates in probability all measurable functions on the boundary of $T$. We also study algebraic genericity, spaceability and frequent universality of these phenomena.
2017
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
Con Impact Factor ISI
Infinite trees, transition coefficients, harmonic functions, boundary of a tree, universal harmonic functions
Abakumov, E., Nestoridis, V., Picardello, A.m. (2017). Universal properties of harmonic functions on trees. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 445(2), 1181-1187 [10.1016/j.jmaa.2016.03.078].
Abakumov, E; Nestoridis, V; Picardello, Am
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/189243
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