Zero-Energy Bound State Decay for Non-local Schrödinger Operators
Sign Up to like & getrecommendations! Published in 2019 at "Communications in Mathematical Physics"
DOI: 10.1007/s00220-019-03515-3
Abstract: We consider solutions of the eigenvalue equation at zero energy for a class of non-local Schrödinger operators with potentials decreasing to zero at infinity. Using a path integral approach, we obtain detailed results on the… read more here.
Keywords: schr dinger; zero energy; dinger operators; local schr ... See more keywords
Trace formulas for Schrödinger operators with complex potentials on a half line
Sign Up to like & getrecommendations! Published in 2019 at "Letters in Mathematical Physics"
DOI: 10.1007/s11005-019-01210-x
Abstract: We consider Schrödinger operators with complex-valued decaying potentials on the half line. Such operator has essential spectrum on the half line plus eigenvalues (counted with algebraic multiplicity) in the complex plane without the positive half… read more here.
Keywords: operators complex; line; half line; dinger operators ... See more keywords
Carleson measures, BMO spaces and balayages associated to Schrödinger operators
Sign Up to like & getrecommendations! Published in 2017 at "Science China Mathematics"
DOI: 10.1007/s11425-016-9147-y
Abstract: Let L be a Schrödinger operator of the form L = −Δ+V acting on L2(Rn), n ≥ 3, where the nonnegative potential V belongs to the reverse Hölder class Bq for some q ≥ n:… read more here.
Keywords: left right; associated schr; dinger operators; right left ... See more keywords
Addendum to “Criticality theory for Schrödinger operators with singular potential” [J. Differ. Equ. 265 (2018) 3400–3440]
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2020.05.031
Abstract: Abstract We show that the cone of non-negative distributional supersolutions is one dimensional for an operator − Δ + V with a locally integrable potential V satisfying property (1.1) below. As a consequence, we obtain… read more here.
Keywords: criticality theory; theory schr; operators singular; dinger operators ... See more keywords
Pointwise dispersive estimates for Schrödinger operators on product cones
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2022.02.060
Abstract: We investigate the dispersive properties of solutions to the Schrodinger equation with a weakly decaying radial potential on cones. If the potential has sufficient polynomial decay at infinity, then we show that the Schrodinger flow… read more here.
Keywords: estimates schr; dinger operators; pointwise dispersive; dispersive estimates ... See more keywords
A note on eigenvalue bounds for Schrödinger operators
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2018.10.006
Abstract: We obtain a new bound on the location of eigenvalues for a non-self-adjoint Schr\"odinger operator with complex-valued potentials by obtaining a weighted $L^2$ estimate for the resolvent of the Laplacian. read more here.
Keywords: schr dinger; bounds schr; dinger operators; eigenvalue bounds ... See more keywords
Spectral Theory of Schrödinger Operators over Circle Diffeomorphisms
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DOI: 10.1093/imrn/rnaa362
Abstract: We initiate the study of Schrödinger operators with ergodic potentials defined over circle map dynamics, in particular over circle diffeomorphisms. For analytic circle diffeomorphisms and a set of rotation numbers satisfying Yoccoz’sH arithmetic condition, we… read more here.
Keywords: schr dinger; circle diffeomorphisms; theory; dinger operators ... See more keywords
Criteria for Embedded Eigenvalues for Discrete Schrödinger Operators
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DOI: 10.1093/imrn/rnz262
Abstract: In this paper, we consider discrete Schrödinger operators of the form, $$\begin{equation*} (Hu)(n) = u({n+1})+u({n-1})+V(n)u(n). \end{equation*}$$We view $H$ as a perturbation of the free operator $H_0$, where $(H_0u)(n)= u({n+1})+u({n-1})$. For $H_0$ (no perturbation), $\sigma _{\textrm{ess}}(H_0)=\sigma… read more here.
Keywords: embedded eigenvalues; dinger operators; discrete schr; criteria embedded ... See more keywords
Eigenvalue Bounds for a Class of Schrödinger Operators in a Strip
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DOI: 10.1155/2018/7172356
Abstract: This paper is concerned with the estimation of the number of negative eigenvalues (bound states) of Schrödinger operators in a strip subject to Neumann boundary conditions. The estimates involve weighted L1 norms and LlnL norms… read more here.
Keywords: eigenvalue bounds; dinger operators; bounds class; operators strip ... See more keywords