Addendum to 'The equivariant spectral function of an invariant elliptic operator'

Abstract

Let $M$ be a compact boundaryless Riemannian manifold, carrying an effective and isometric action of a torus $T$, and $P_0$ an invariant elliptic classical pseudodifferential operator on $M$. In this note, we strengthen asymptotics for the equivariant (or reduced) spectral function of $P_0$ derived previously, which are already sharp in the eigenvalue aspect, to become almost sharp in the isotypic aspect. In particular, this leads to hybrid equivariant $L^p$-bounds for eigenfunctions that are almost sharp in the eigenvalue and isotypic aspect.

14 pages. arXiv admin note: text overlap with arXiv:1512.02193

References in corpus (1)

• Subconvex bounds for Hecke-Maass forms on compact arithmetic quotients of semisimple Lie groups