Information geometry of Poisson kernels on Damek-Ricci spaces

DOI10.3836/TJM/1279719582zbMath1196.53034OpenAlexW1977372486MaRDI QIDQ989204

Mitsuhiro Itoh, Hiroyasu Satoh

Publication date: 30 August 2010

Published in: Tokyo Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3836/tjm/1279719582

zbMATH Keywords

Fisher informationPoisson kernelDamek-Ricci space

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Harmonic analysis on homogeneous spaces (43A85) Differential geometry of symmetric spaces (53C35)

Related Items (8)

Harmonic functions on rank one asymptotically harmonic manifolds ⋮ Harmonic manifolds of hypergeometric type and spherical Fourier transform ⋮ Geometric mean of probability measures and geodesics of Fisher information metric ⋮ Fisher information geometry, Poisson kernel and asymptotical harmonicity ⋮ Radon transform on a harmonic manifold ⋮ Information geometry of Busemann-barycenter for probability measures ⋮ Information geometry of the space of probability measures and barycenter maps ⋮ Horospheres and hyperbolicity of Hadamard manifolds

Cites Work

• Harmonic measures and Bowen-Margulis measures
• Fisher information metric and Poisson kernels
• Homogeneous Riemannian manifolds and the visibility axiom
• Manifolds of nonpositive curvature
• Harmonic analysis on solvable extensions of H-type groups
• Generalized Heisenberg groups and Damek-Ricci harmonic spaces
• A Poisson kernel on Heisenberg type nilpotent groups
• Die Fisher-Information und symplektische Strukturen
• On the curvature of certain extensions of $H$-type groups
• On the Volume Elements on a Manifold
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