Spherical functions on homogeneous tree
WebConsider an infinite homogeneous tree T n of valence n+ 1, its group Aut(T n) of auto-morphisms, and the group Hier(T ... In other words, a spherical function is defined on the double coset space K \G/K. Definition 1.1. Let G be a topological group, K a closed subgroup. The subgroup WebA function (b defined on F, is callled spherical if: (1) Q is radial; (2) 4 *f = cd for every fE -t4, where c is a constant depending on f and 4; (3) 4(e) = 1. If f is any function on F,., we …
Spherical functions on homogeneous tree
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WebOlshanski spherical pairs consisting of automorphism groups for a homogeneous tree and a homogeneous rooted tree, respectively. We determine the spherical functions, discuss their positive definiteness, and make realizations of the corresponding spherical representations. WebJan 1, 2006 · Spherical Function; Convolution Operator; Homogeneous Tree; These keywords were added by machine and not by the authors. This process is experimental …
WebThe spherical functions on Γ are simply the spherical functions on the homogeneous tree (Γ, e), where we have identified (the vertices of) the Cayley graph with Γ. In section 4 we use Theorem 0.2 and 0.3 to prove similar results about Fourier multipliers and spherical functions on groups Γ of the form (0.4) (cf. Theorem 4.2 and 4.4). WebSpherical harmonics are a set of functions used to represent functions on the surface of the sphere S^2 S 2. They are a higher-dimensional analogy of Fourier series, which form a complete basis for the set of periodic …
WebAbstract. On a semi-homogeneous tree, we study the ‘p-spectrum of the Laplace operator 1 (the isotropic nearest-neighbor transition operator); the known results in the much simpler setting of homogeneous trees are obtained as particular cases. The spectrum is given by the eigenvalues of spherical functions, i.e., eigenfunc-tions of WebA homogeneous tree X of degree q+ 1 is de ned to be a connected graph with no loops, in which every vertex is adjacent to q+1 other vertices. ... {Beltrami operator, spherical functions, harmonic analysis. Work partially supported by the Australian Research Council and the Italian M.U.R.S.T. c 2000 American Mathematical Society 4271
WebFeb 1, 2003 · The limit functions have interpretations as spherical functions on homogeneous trees (see references in [4, p. 28]) and on infinite distance-transitive graphs (see [30] ). Note that...
WebApr 9, 2009 · Let G be a group acting faithfully on a homogeneous tree of order p + 1, p > 1. Let be the space of functions on the Poission boundary ω, of zero mean on ω. When p is a prime. ... A. J., PGL 2 over the p-adics: its representations, spherical functions, and Fourier analysis (Lecture Notes in Math. 166, Springer-Verlag, Berlin, Heidelberg, ... is there a problem with dvla websiteWebWe describe their convolution kernels in comparison with those of the corresponding operators on a homogeneous tree T, separately studied as acting on functions on the … is there a problem with earthlink mailWebWe shall define the spectral projection on the homogeneous tree $\\mathfrak X$, which is an analogue of the one given by Bray for semisimple Lie groups. We shall prove the Paley--Wiener theorem for the spectral projection on $\\mathfrak X$. As an application, we present an elementary proof of the Paley--Wiener theorem for the Helgason--Fourier transform on … iis latin meaningWebAug 31, 2009 · Schur Multipliers and Spherical Functions on Homogeneous Trees Uffe Haagerup, Troels Steenstrup, Ryszard Szwarc Let X be a homogeneous tree of degree q+1 … iis launch settingsWebthe Bergman spaces of harmonic functions on a homogeneous tree and define the measure classes under consideration in our work in terms of certain Carleson-type conditions. We … i island hopping honeymoon packagesWebSpherical functions and radial functions on free groups have been studied by Cartier [3,4] and Sawyer [23] in the context of random walks on ... G of isometries of a homogeneous tree (endowed with its natural metric). This group is the product of a compact subgroup K and a closed subgroup . SPHERICAL ... is there a problem with duolingoWebon homogeneous tree. Our proof is based on the duality argument and the norm estimates of ... The above estimates of spherical function are well known and can be found in the literature (see e.g.[2, 3] and the reference given there in). … is there a problem with ebt cards