Spectral cluster bounds for orthonormal systems and oscillatory integral   operators in Schatten spaces
  We generalize the $L^p$ 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. 
Rupert L. Frank, Julien Sabin
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