4 citations · 4 across the 6 of their papers we have counts for
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Unconditional wave decay in dimension two
T. J. Christiansen, K. Datchev, P. Morales +1
We extend Burq's logarithmic decay rate [Bur98] to general compactly supported scatterers in dimension two. The main novelty is using recent results on low-frequency expansions to…
From resolvent expansions at zero to long time wave expansions
T. J. Christiansen, K. Datchev, M. Yang
We prove a general abstract theorem deducing wave expansions as time goes to infinity from resolvent expansions as energy goes to zero, under an assumption of polynomial boundednes…
Low energy resolvent asymptotics of the multipole Aharonov--Bohm Hamiltonian
T. J. Christiansen, K. Datchev, M. Yang
We compute low energy asymptotics for the resolvent of the Aharonov--Bohm Hamiltonian with multiple poles for both integer and non-integer total fluxes. For integral total flux we…
Low energy resolvent expansions in dimension two
T. J. Christiansen, K. Datchev
The behavior of the resolvent at low energies has implications for many kinds of asymptotics, including for the scattering matrix and phase, for the Dirichlet-to-Neumann map, and f…
Resolvent estimates on asymptotically cylindrical manifolds and on the half line
T. J. Christiansen, K. Datchev
Manifolds with infinite cylindrical ends have continuous spectrum of increasing multiplicity as energy grows, and in general embedded resonances (resonances on the real line, embed…