Spectral cluster bounds for orthonormal systems and oscillatory integral operators in Schatten spaces
Analysis of PDEs
2016-08-31 v1 Classical Analysis and ODEs
Spectral Theory
Abstract
We generalize the spectral cluster bounds of Sogge for the Laplace-Beltrami operator on compact Riemannian manifolds to systems of orthonormal functions. The optimality of these new bounds is also discussed. These spectral cluster bounds follow from Schatten-type bounds on oscillatory integral operators.
Keywords
Cite
@article{arxiv.1608.08299,
title = {Spectral cluster bounds for orthonormal systems and oscillatory integral operators in Schatten spaces},
author = {Rupert L. Frank and Julien Sabin},
journal= {arXiv preprint arXiv:1608.08299},
year = {2016}
}
Comments
30 pages