\(L^2\)-concrete spectral analysis of the invariant Laplacian \(\Delta_{\alpha\beta}\) in the unit complex ball \(B^n\)

DOI10.1006/jfan.1998.3318zbMath0924.43009OpenAlexW2012564862MaRDI QIDQ1276406

Abdelhamid Boussejra, Ahmed Intissar

Publication date: 18 May 1999

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.1998.3318

zbMATH Keywords

Plancherel formulaspherical harmonicseigenfunctionsPoisson integralJacobi functionsCalderon-Zygmund theory

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Harmonic analysis on homogeneous spaces (43A85) Integral representations of solutions to PDEs (35C15) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25)

Related Items (9)

Lifted infinitesimal holomorphic representation for the \(n\)-dimensional complex hyperbolic ball and for Cartan domains of type I ⋮ Solving the heat equation for a perturbed magnetic Laplacian on the complex plane ⋮ Ornstein-Uhlenbeck operators and holomorphic representations for a class of bounded symmetric domains ⋮ A characterization of the \(L^2\)-range of the Poisson transforms on a class of vector bundles over the quaternionic hyperbolic spaces ⋮ Fractional Zernike functions ⋮ Asymptotic of complex hyperbolic geometry and L2-spectral analysis of Landau-like Hamiltonians ⋮ Selberg trace formulae for heat and wave kernels of Maass Laplacians on compact forms of the complex hyperbolic space \(H^n(\mathbb C)\), \(n\geq 2\) ⋮ Spectral density for the Schrödinger operator with magnetic field in the unit complex ball: solutions of evolutionary equations and applications to special functions ⋮ \(L^2\)-Poisson integral representations of eigensections of invariant differential operators on a homogeneous line bundle over the complex Grassmann manifold \(SU(r,r+b)/S( U(r)\times U(r+b))\)

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