Eigenfunctions of the Laplace-Beltrami Operator on Hyperboloids
Amritanshu Prasad, M. K. Vemuri
TL;DR
This paper investigates eigenfunctions of the Laplace-Beltrami operator on hyperboloids, providing insights similar to spherical harmonics and offering a new proof for a Legendre function integral.
Contribution
It introduces a novel analysis of Laplace-Beltrami eigenfunctions on hyperboloids and presents a simplified proof of Laplace's integral for Legendre functions.
Findings
Eigenfunctions characterized on hyperboloids
A new proof of Laplace's integral for Legendre functions
Connections to spherical harmonics analysis
Abstract
Eigenfunctions of the Laplace-Beltrami operator on a hyperboloid are studied in the spirit of the treatment of the spherical harmonics by Stein and Weiss. As a special case, a simple self-contained proof of Laplace's integral for a Legendre function is obtained.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNumerical methods in inverse problems · Algebraic and Geometric Analysis · advanced mathematical theories