Characterization of eigenfunctions of the Laplace-Beltrami operator through heat propagation in small time

DOI10.1007/s00605-020-01437-0zbMath1451.58012OpenAlexW3038065904MaRDI QIDQ779993

Rudra P. Sarkar, Muna Naik

Publication date: 14 July 2020

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-020-01437-0

zbMATH Keywords

heat kernelRiemannian symmetric spaceseigenfunction of the Laplace-Beltrami operator

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Harmonic analysis on homogeneous spaces (43A85) Analysis on real and complex Lie groups (22E30) Differential geometry of symmetric spaces (53C35) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items

Characterization of eigenfunctions of the Laplace-Beltrami operator using Fourier multipliers

Cites Work

• A characterization of the \(L^{2}\)-range of the Poisson transform related to Strichartz conjecture on symmetric spaces of noncompact type
• \(L^ p\)-estimates on functions of the Laplace operator
• The spherical Fourier transform of rapidly decreasing functions. A simple proof of a characterization due to Harish-Chandra, Helgason, Trombi, and Varadarajan
• Harmonic analysis as spectral theory of Laplacians
• Harmonic analysis on solvable extensions of H-type groups
• On the Fourier transform of rapidly decreasing functions of \(L^p\) type on a symmetric space
• Eigenfunctions of invariant differential operators on a symmetric space
• Integrable harmonic functions on symmetric spaces of rank one
• Harmonic functions with polynomial growth
• An endpoint estimate for the Kunze-Stein phenomenon and related maximal operators
• The injectivity of the Pompeiu transform and \(L^ p\)-analogues of the Wiener-Tauberian theorem
• On Furstenberg's characterization of harmonic functions on symmetric spaces
• Heat kernel and Green function estimates on noncompact symmetric spaces
• Fourier restriction theorem and characterization of weak \(L^2\) eigenfunctions of the Laplace-Beltrami operator
• A Poisson formula for semi-simple Lie groups
• Eigenfunctions of the Laplace-Beltrami operator on harmonic \(NA\) groups
• Characterisations of Poisson integrals on symmetric spaces.
• Harmonic functions on complete riemannian manifolds
• Differential equations on riemannian manifolds and their geometric applications
• Characterization of almost 𝐿^{𝑝}-eigenfunctions of the Laplace-Beltrami operator
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item