PreprintCC BY 4.0arXiv
Off-diagonal bounds for spectral projector kernels
Abstract
We study the growth of the spectral function of the Laplace-Beltrami operator on a Riemannian manifold M of dimension n. For n≥ 3 we show that for any x∈ M there is a full measure subset Zx⊂ M such that for all y∈ Zx EΛ(x,y) = OM,x,y,ε(Λn/2(logΛ)3/2(loglogΛ)1/2+ε). For n=2 we prove a stronger statement. For any x∈ M there is a full measure subset Zx⊂ M such that for all y∈ Zx EΛ(x,y) = OM,x,y,ε(Λ5/6(logΛ)1/6(loglogΛ)1/6+ε) .
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BibTeX
@misc{dimakis2026offdiagonal,
title = {{Off-diagonal bounds for spectral projector kernels}},
author = {Panagiotis Dimakis},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33957},
eprint = {2609.33957},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33957},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Off-diagonal bounds for spectral projector kernels
AU - Panagiotis Dimakis
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33957
UR - https://arxiv.org/abs/2609.33957
AB - We study the growth of the spectral function of the Laplace-Beltrami operator on a Riemannian manifold M of dimension n. For n≥ 3 we show that for any x∈ M there is a full measure subset Z_x⊂ M such that for all y∈ Z_x E_Λ(x,y) = O_M,x,y,ε(Λ^n/2(logΛ)^3/2(loglogΛ)^1/2+ε). For n=2 we prove a stronger statement. For any x∈ M there is a full measure subset Z_x⊂ M such that for all y∈ Z_x E_Λ(x,y) = O_M,x,y,ε(Λ^5/6(logΛ)^1/6(loglogΛ)^1/6+ε) .
ER -