{"paper":{"title":"The equivariant spectral function of an invariant elliptic operator. $L^p$-bounds, caustics, and concentration of eigenfunctions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Pablo Ramacher","submitted_at":"2015-12-07T20:25:26Z","abstract_excerpt":"Let $M$ be a compact boundaryless Riemannian manifold, carrying an effective and isometric action of a compact Lie group $G$, and $P_0$ an invariant elliptic classical pseudodifferential operator on $M$. Using Fourier integral operator techniques, we prove a local Weyl law with remainder estimate for the equivariant (or reduced) spectral function of $P_0$ for each isotpyic component in the Peter-Weyl decomposition of $L^2(M)$, generalizing work of Avacumovi\\v{c}, Levitan, and H\\\"ormander. From this we deduce a generalized Kuznecov sum formula for periods of G-orbits, and recover the local Weyl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02193","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}