Harmonic analysis for vector fields on hyperbolic spaces

DOI10.1007/BF01159971zbMath0662.43011MaRDI QIDQ1113416

Erich Badertscher, Hans Martin Reimann

Publication date: 1989

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/174102

zbMATH Keywords

Plancherel measureinversion formulaPaley-Wiener theoreminvariant differential operatorsvector fieldsspherical systemsJacobi functionsspherical transformHelgason's Fourier transform

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Vector fields, frame fields in differential topology (57R25) Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Geodesics in global differential geometry (53C22) Other transforms and operators of Fourier type (43A32) Harmonic analysis and spherical functions (43A90)

Related Items (5)

The Plancherel measure for \(p\)-forms in real hyperbolic spaces ⋮ Ray-Singer torsion for a hyperbolic 3-manifold and asymptotics of Chern-Simons-Witten invariant ⋮ Spectral functions and zeta functions in hyperbolic spaces ⋮ Invariant syzygies and semisimple groups ⋮ Clifford–Fourier transform on hyperbolic space

Cites Work

• Transformation de Poisson de formes différentielles. Le cas de l'espace hyperbolique. (Poisson transformation of differential forms. The case of hyperbolic space)
• Quasiconformal deformations and mappings in \(\mathbb R^n\)
• Générateurs de l'algèbre ${\cal U}(G)^K$ avec $G=SO(m)$ ou $SO_0(1,m-1)$ et $K=SO(m-1)$
• Invariant operators and integral representations in hyperbolic space.
• Generalization of the Cauchy-Riemann Equations and Representations of the Rotation Group
• The Plancherel formula for the Lorentz group of $n$-th order
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