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Frank, Rupert L. and Sabin, Julien (2017): Spectral cluster bounds for orthonormal systems and oscillatory integral operators in Schatten spaces. In: Advances in Mathematics, Vol. 317: pp. 157-192

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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.

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