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Harmonic analysis for spinors on real hyperbolic spaces

Roberto Camporesi, Emmanuel Pedon (2001)

Colloquium Mathematicae

We develop the L² harmonic analysis for (Dirac) spinors on the real hyperbolic space Hⁿ(ℝ) and give the analogue of the classical notions and results known for functions and differential forms: we investigate the Poisson transform, spherical function theory, spherical Fourier transform and Fourier transform. Very explicit expressions and statements are obtained by reduction to Jacobi analysis on L²(ℝ). As applications, we describe the exact spectrum of the Dirac operator, study the Abel transform...

Harmonic analysis of spherical functions on S U ( 1 , 1 )

Y. Benyamini, Yitzhak Weit (1992)

Annales de l'institut Fourier

Denote by L 1 ( K ∖ G / K ) the algebra of spherical integrable functions on S U ( 1 , 1 ) , with convolution as multiplication. This is a commutative semi-simple algebra, and we use its Gelfand transform to study the ideals in L 1 ( K ∖ G / K ) . In particular, we are interested in conditions on an ideal that ensure that it is all of L 1 ( K ∖ G / K ) , or that it is L 0 1 ( K ∖ G / K ) . Spherical functions on S U ( 1 , 1 ) are naturally represented as radial functions on the unit disk D in the complex plane. Using this representation, these results are applied to characterize harmonic...

Harmonic analysis of symmetric random graphs

Steffen Lauritzen (2020)

Kybernetika

This note attempts to understand graph limits as defined by Lovasz and Szegedy in terms of harmonic analysis on semigroups. This is done by representing probability distributions of random exchangeable graphs as mixtures of characters on the semigroup of unlabeled graphs with node-disjoint union, thereby providing an alternative derivation of de Finetti's theorem for random exchangeable graphs.

Harmonic functions on the real hyperbolic ball I: Boundary values and atomic decomposition of Hardy spaces

Philippe Jaming (1999)

Colloquium Mathematicae

We study harmonic functions for the Laplace-eltrami operator on the real hyperbolic space n . We obtain necessary and sufficient conditions for these functions and their normal derivatives to have a boundary distribution. In doing so, we consider different behaviors of hyperbolic harmonic functions according to the parity of the dimension of the hyperbolic ball n . We then study the Hardy spaces H p ( n ) , 0

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