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.
The spectral function of an elliptic operator
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The harmonic ensemble achieves optimal Wasserstein equidistribution rates on homogeneous manifolds of dimension d≥3 and two-point homogeneous manifolds, with similar results for the spherical ensemble and GAF zeros.
The survey describes eigenvalue inequalities, spectral asymptotics, nodal domains, and new phenomena for the Dirichlet-to-Neumann map of the Helmholtz equation that do not appear in the Laplace case.
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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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Spectral properties of the Dirichlet-to-Neumann map for the Helmholtz equation
The survey describes eigenvalue inequalities, spectral asymptotics, nodal domains, and new phenomena for the Dirichlet-to-Neumann map of the Helmholtz equation that do not appear in the Laplace case.