Universal properties of harmonic functions on trees

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:445

Article

Abakumov, Evgeny¹  Nestoridis, Vassili²  Picardello, Massimo A.³ 

[1] Univ Paris Est, LAMA UMR 8050, F-77454 Marne La Vallee, France

[2] Univ Athens, Dept Math, Panepistimioupolis, GR-15784 Athens, Greece

[3] Univ Roma Tor Vergata, Dipartimento Matemat, Via Ric Sci, I-00133 Rome, Italy

关键词: Infinite trees;    Transition coefficients;    Harmonic functions;    Boundary of a tree;    Universal harmonic functions;   

DOI  :  10.1016/j.jmaa.2016.03.078

来源: Elsevier

【 摘 要 】

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 C. 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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free