\(L^p\) norms of higher rank eigenfunctions and bounds for spherical functions

DOI10.4171/JEMS/619zbMath1344.22003arXiv1106.0534OpenAlexW3103777076MaRDI QIDQ726754

Simon Marshall

Publication date: 14 July 2016

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.0534

zbMATH Keywords

spherical functionssymmetric spaces\(L^p\)-norms

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) Analysis on real and complex Lie groups (22E30)

Related Items (10)

The equivariant spectral function of an invariant elliptic operator. \(L^p\)-bounds, caustics, and concentration of eigenfunctions ⋮ The \(L^2\) restriction norm of a Maass form on \(\mathrm{SL}_{n+1}(\mathbb {Z})\) ⋮ Distribution of Hecke Eigenvalues for GL(n) ⋮ On Fourier restriction type problems on compact Lie groups ⋮ Large values of eigenfunctions on arithmetic hyperbolic 3-manifolds ⋮ Schrödinger equations on compact globally symmetric spaces ⋮ Sato-Tate equidistribution for families of Hecke-Maass forms on \(\mathrm{SL}(n,\mathbb{R})/\mathrm{SO}(n)\) ⋮ Special value formula for the twisted triple product \(L\)-function and an application to the restricted \(L^2\)-norm problem ⋮ \(L^p\) estimates for joint quasimodes of semiclassical pseudodifferential operators ⋮ Local \(L^p\) norms of Schrödinger eigenfunctions on \({\mathbb{S}}^2\)

Cites Work

• Über die Eigenfunktionen auf geschlossenen Riemannschen Mannigfaltigkeiten
• Restrictions of the Laplace-Beltrami eigenfunctions to submanifolds
• Concerning the \(L^ p\) norm of spectral clusters for second-order elliptic operators on compact manifolds
• Riemannian manifolds with uniformly bounded eigenfunctions
• On quantum unique ergodicity for locally symmetric spaces
• On the Plancherel formula and the Paley-Wiener theorem for spherical functions on semisimple Lie groups
• The sup-norm problem on the Siegel modular space of rank two
• A restriction theorem for the Fourier transform
• Introduction to Singularities and Deformations
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