Harmonic analysis on solvable extensions of H-type groups

DOI10.1007/BF02921294zbMath0788.43008OpenAlexW2053947267MaRDI QIDQ1188262

Fulvio Ricci, Ewa Damek

Publication date: 13 August 1992

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02921294

zbMATH Keywords

spherical functionsMartin boundaryGelfand pairsLie algebraLie groupLaplace-Beltrami operatoraveraging operatorhypergeometric differential equationconvolution algebraLichnerowicz conjectureRiemannian symmetric spacegeneralized Cayley transformharmonic Riemannian manifoldintegrable radial functionsnilpotent \(H\)-group

Mathematics Subject Classification ID

Martin boundary theory (31C35) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Nilpotent and solvable Lie groups (22E25) Analysis on other specific Lie groups (43A80) Harmonic analysis and spherical functions (43A90) (L^1)-algebras on groups, semigroups, etc. (43A20)

Related Items (94)

The angular Laplacian on symmetric Damek-Ricci spaces ⋮ Geodesic inversion and Sobolev spaces on Heisenberg type groups ⋮ Spherical spectral synthesis and two-radius theorems on Damek-Ricci spaces ⋮ Pointwise estimates for the Poisson kernel on \(NA\) groups by the Ancona method ⋮ Decay estimates for fractional wave equations on \(H\)-type groups ⋮ Multipliers for a distinguished Laplacean on solvable extensions of \(H\)-type groups ⋮ Asymptotic mean value property for eigenfunctions of the Laplace-Beltrami operator on Damek-Ricci spaces ⋮ Marcinkiewicz multipliers and multi-parameter structure on Heisenberg (-type) groups. II ⋮ A note on \(K\)-functional, modulus of smoothness, Jackson theorem and Bernstein-Nikolskii-Stechkin inequality on Damek-Ricci spaces ⋮ Fourier and Radon transform on harmonic 𝑁𝐴 groups ⋮ TANGENTIAL CONVERGENCE OF BOUNDED HARMONIC FUNCTIONS ON GENERALIZED SIEGEL DOMAINS ⋮ Unnamed Item ⋮ Spectral multipliers on 2-step stratified groups. II ⋮ Spectral multipliers for Laplacians with drift on Damek-Ricci spaces ⋮ Entire solutions to sublinear elliptic problems on harmonic \textit{NA} groups and Euclidean spaces ⋮ Chaotic dynamics of the heat semigroup on the Damek-Ricci spaces ⋮ A class of nonsymmetric harmonic Riemannian spaces ⋮ SOME -HARDY AND -RELLICH TYPE INEQUALITIES WITH REMAINDER TERMS ⋮ The Dirichlet problem for harmonic maps between Damek-Ricci spaces ⋮ Harmonic manifolds with some specific volume densities ⋮ Two functionals connected to the Laplacian in a class of doubly connected domains on rank one symmetric spaces of non-compact type ⋮ Harmonic manifolds of hypergeometric type and spherical Fourier transform ⋮ Huygens' principle and a Paley-Wiener type theorem on Damek-Ricci spaces ⋮ ON THE ALGEBRAS AND OF AN ULTRASPHERICAL HYPERGROUP ⋮ Paley-Wiener theorems for the \(\mathrm U(n)\)-spherical transform on the Heisenberg group ⋮ Semi-classical analysis on H-type groups ⋮ Sharp Hardy-Littlewood-Sobolev inequalities on quaternionic Heisenberg groups ⋮ Inclusions and noninclusions of Hardy type spaces on certain nondoubling manifolds ⋮ Fatou theorem and its converse for positive eigenfunctions of the Laplace-Beltrami operator on harmonic \textit{NA} groups ⋮ On harmonic and 2-stein spaces of Iwasawa type. ⋮ Existence of isometric immersions into nilpotent Lie groups ⋮ The shifted wave equation on non-flat harmonic manifolds ⋮ Scalar products on Clifford modules and pseudo-\(H\)-type Lie algebras ⋮ On the curvature of certain extensions of $H$-type groups ⋮ Nilpotent Gelfand pairs and spherical transforms of Schwartz functions. 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