Fourier Method for One Dimensional Schrödinger Operators with Singular Periodic Potentials
نویسنده
چکیده
By using quasi–derivatives, we develop a Fourier method for studying the spectral properties of one dimensional Schrödinger operators with periodic singular potentials.
منابع مشابه
Spectral gaps of Schrödinger operators with periodic singular potentials
By using quasi–derivatives we develop a Fourier method for studying the spectral gaps of one dimensional Schrödinger operators with periodic singular potentials v. Our results reveal a close relationship between smoothness of potentials and spectral gap asymptotics under a priori assumption v ∈ H loc (R). They extend and strengthen similar results proved in the classical case v ∈ L loc (R).
متن کاملOperators with Singular Continuous Spectrum: Iii. Almost Periodic Schrödinger Operators
We prove that one-dimensional Schrödinger operators with even almost periodic potential have no point spectrum for a dense Gδ in the hull. This implies purely singular continuous spectrum for the almost Mathieu equation for coupling larger than 2 and a dense Gδ in θ even if the frequency is an irrational with good Diophantine properties. §
متن کاملInverse Scattering Theory for One-dimensional Schrödinger Operators with Steplike Periodic Potentials
We develop direct and inverse scattering theory for one-dimensional Schrödinger operators with steplike potentials which are asymptotically close to different finite-gap periodic potentials on different half-axes. We give a complete characterization of the scattering data, which allow unique solvability of the inverse scattering problem in the class of perturbations with finite second moment.
متن کاملWave Operator Bounds for 1-dimensional Schrödinger Operators with Singular Potentials and Applications
Boundedness of wave operators for Schrödinger operators in one space dimension for a class of singular potentials, admitting finitely many Dirac delta distributions, is proved. Applications are presented to, for example, dispersive estimates and commutator bounds.
متن کاملDispersion Estimates for One-dimensional Schrödinger Equations with Singular Potentials
We derive a dispersion estimate for one-dimensional perturbed radial Schrödinger operators. We also derive several new estimates for solutions of the underlying differential equation and investigate the behavior of the Jost function near the edge of the continuous spectrum.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008