Exact log growth exponents of L^p norms (1 to infinity) for disk eigenfunctions are determined, along with sharp uniform upper and lower bounds, via stationary phase and Bessel integral estimates.
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Proves the orthonormal analogue of Hassell-Tacy log-improved L^q spectral cluster bounds for windows of width (log λ)^{-1} on closed n-manifolds with nonpositive sectional curvature by combining Frank-Sabin orthonormal bounds, Bérard kernel estimates, and a generalized Bourgain-Shao-Sogge-Yao multip
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Exact $L^p$ growth rates of Laplace eigenfunctions on the unit disk
Exact log growth exponents of L^p norms (1 to infinity) for disk eigenfunctions are determined, along with sharp uniform upper and lower bounds, via stationary phase and Bessel integral estimates.
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Orthonormal Spectral Cluster Bounds on Manifolds with Nonpositive Curvature
Proves the orthonormal analogue of Hassell-Tacy log-improved L^q spectral cluster bounds for windows of width (log λ)^{-1} on closed n-manifolds with nonpositive sectional curvature by combining Frank-Sabin orthonormal bounds, Bérard kernel estimates, and a generalized Bourgain-Shao-Sogge-Yao multip