6 papers
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…
Persistence and disappearance of negative eigenvalues in dimension two
T. J. Christiansen, K. Datchev, C. Griffin
We compute asymptotics of eigenvalues approaching the bottom of the continuous spectrum, and associated resonances, for Schrödinger operators in dimension two. We distinguish persi…
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…
Singularities and asymptotic distribution of resonances for Schrödinger operators in one dimension
T. J. Christiansen, T. Cunningham
We obtain new results about the high-energy distribution of resonances for the one-dimensional Schrödinger operator. Our primary result is an upper bound on the density of resonanc…