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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Displaying similar documents to “Poisson kernels of drifted Laplace operators on trees and on the half-plane”
Boundary behaviour of eigenfunctions of the Laplace operator on trees
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We apply the Feynman-Kac formula to compute the λ-Poisson kernels and λ-Green functions for half-spaces or balls in hyperbolic spaces. We present known results in a unified way and also provide new formulas for the λ-Poisson kernels and λ-Green functions of half-spaces in ℍⁿ and for balls in real and complex hyperbolic spaces.
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This paper is a contribution to the general tiling problem for the hyperbolic plane. It is an intermediary result between the result obtained by R. Robinson [ (1978) 259–264] and the conjecture that the problem is undecidable.
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Electronic Research Announcements of the American Mathematical Society [electronic only]
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The aim of this paper is to give a description of the Poisson kernel and the Green function of balls in the complex hyperbolic space. The description is in terms of the hypergeometric function and unitary spherical harmonics in ℂⁿ.
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Santaló, L.A. (1980)
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The Poisson Boundary of the Mapping Class Group and of Teichmüller Space
Vadim A. Kaimanovich, Howard Masur (1994)
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Computation of Biharmonic Poisson Kernel for the Upper Half Plane
Ali Abkar (2007)
Bollettino dell'Unione Matematica Italiana
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We first consider the biharmonic Poisson kernel for the unit disk, and study the boundary behavior of potentials associated to this kernel function. We shall then use some properties of the biharmonic Poisson kernel for the unit disk to compute the analogous biharmonic Poisson kernel for the upper half plane.
Poisson trees, succession lines and coalescing random walks
P. A. Ferrari, C. Landim, H. Thorisson (2004)
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Poisson transforms for differential forms
Christoph Harrach (2016)
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We give a construction of a Poisson transform mapping density valued differential forms on generalized flag manifolds to differential forms on the corresponding Riemannian symmetric spaces, which can be described entirely in terms of finite dimensional representations of reductive Lie groups. Moreover, we will explicitly generate a family of degree-preserving Poisson transforms whose restriction to real valued differential forms has coclosed images. In addition, as a transform on sections...
On the area of a polygon in the hyperbolic plane.
Kántor, Sándor (1998)
Beiträge zur Algebra und Geometrie
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Limit distributions and random trees derived from the birthday problem with unequal probabilities.
Camarri, Michael, Pitman, Jim (2000)
Electronic Journal of Probability [electronic only]
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The Markovian hyperbolic triangulation
Nicolas Curien, Wendelin Werner (2013)
Journal of the European Mathematical Society
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We construct and study the unique random tiling of the hyperbolic plane into ideal hyperbolic triangles (with the three corners located on the boundary) that is invariant (in law) with respect to Möbius transformations, and possesses a natural spatial Markov property that can be roughly described as the conditional independence of the two parts of the triangulation on the two sides of the edge of one of its triangles.