Restriction of eigenfunctions on products of spheres to submanifolds of maximal flats
Abstract
Let M M be a product of rank-one symmetric spaces of compact type, each of dimension at least 3 3 . We establish sharp L p L^p bounds for the restriction of Laplace–Beltrami eigenfunctions on M M to arbitrary submanifolds contained in a maximal flat, for all p ≥ 2 p \ge 2 . The proof combines precise asymptotics of Jacobi polynomials and positivity of Fourier coefficients of spherical functions.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Mathematical Analysis and Transform Methods
Advanced Algebra and Geometry
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Publication date
- 5 March 2026
- Language
- EN