Short-time rescalings of compression covariance defects E_s,t = V_s^* V_t yield tangent kernels F whose Kolmogorov spaces carry induced contraction semigroups whose representing vectors obey additive cocycle identities, restricting admissible positive kernels.
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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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Compression Covariance and Tangent kernels
Short-time rescalings of compression covariance defects E_s,t = V_s^* V_t yield tangent kernels F whose Kolmogorov spaces carry induced contraction semigroups whose representing vectors obey additive cocycle identities, restricting admissible positive kernels.
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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.