Boundary behaviour of eigenfunctions of the Laplace operator on trees
Adam Korányi, Massimo A. Picardello (1986)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Adam Korányi, Massimo A. Picardello (1986)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Tadeusz Pytlik (1992)
Colloquium Mathematicae
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Wolfgang Woess (1995)
Monatshefte für Mathematik
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Konrad Kolesko (2010)
Colloquium Mathematicae
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Let Aff(𝕋) be the group of isometries of a homogeneous tree 𝕋 fixing an end of its boundary. Given a probability measure on Aff(𝕋) we consider an associated random process on the tree. It is known that under suitable hypothesis this random process converges to the boundary of the tree defining a harmonic measure there. In this paper we study the asymptotic behaviour of this measure.
Casadio Tarabusi, Enrico, Cohen, Joel M., Korányi, Adam, Picardello, Massimo A. (1998)
Journal of Lie Theory
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Fausto Di Biase, Massimo A. Picardello (1995)
Mathematische Zeitschrift
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Richard Penney, Roman Urban (2002)
Colloquium Mathematicae
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We study unbounded harmonic functions for a second order differential operator on a homogeneous manifold of negative curvature which is a semidirect product of a nilpotent Lie group N and A = ℝ⁺. We prove that if F is harmonic and satisfies some growth condition then F has an asymptotic expansion as a → 0 with coefficients from 𝓓'(N). Then we single out a set of at most two of these coefficients which determine F. Then using asymptotic expansions we are able to prove...
Frank Beatrous (1991)
Studia Mathematica
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Kaufman, Robert, Llorente, José G., Wu, Jang-Mei (2003)
Annales Academiae Scientiarum Fennicae. Mathematica
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Joaquim Bruna (1992)
Publicacions Matemàtiques
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We prove a boundary uniqueness theorem for harmonic functions with respect to Bergman metric in the unit ball of C and give an application to a Runge type approximation theorem for such functions.
Wen Sheng Wang (1995)
Revista Matemática Iberoamericana
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In any C domain, there is nonzero harmonic function C continuous up to the boundary such that the function and its gradient on the boundary vanish on a set of positive measure.
Philippe Jaming (2001)
Bollettino dell'Unione Matematica Italiana
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In questo articolo studieremo le relazioni fra le funzioni armoniche nella palla iperbolica (sia essa reale, complessa o quaternionica), le funzione armoniche euclidee in questa palla, e le funzione pluriarmoniche sotto certe condizioni di crescita. In particolare, estenderemo al caso quaternionico risultati anteriori dell'autore (nel caso reale), e di A. Bonami, J. Bruna e S. Grellier (nel caso complesso).