相关论文: Borg-Type Theorems for Matrix-Valued Schr\"{o}ding…

We establish quantitative upper and lower bounds for Schr\"odinger operators with complex potentials that satisfy some weak form of sparsity. Our first result is a quantitative version of an example, due to S.\ Boegli (Comm. Math. Phys.,…

We discuss Schr\"odinger operators on a half-line with decaying oscillatory potentials, such as products of an almost periodic function and a decaying function. We provide sufficient conditions for preservation of absolutely continuous…

In this survey we discuss spectral and quantum dynamical properties of discrete one-dimensional Schr\"odinger operators whose potentials are obtained by real-valued sampling along the orbits of an ergodic invertible transformation. After an…

Following the proof given by Froese and Herbst in [FH82] with another conjugate operator, we show for a class of real potential that possible eigenfunction of the Schr\"odinger operator has to decay sub-exponentially. We also show that, for…

Estimates for eigenvalues of Schr\"{o}dinger operators on the half-line with complex-valued potentials are established. Schr\"{o}dinger operators with potentials belonging to weak Lebesque's classes are also considered. The results cover…

We study the stationary scattering theory for the matrix Schr\"odinger equation on the half line, with the most general boundary condition at the origin, and with integrable selfadjoint matrix potentials. We prove the limiting absorption…

We develop direct scattering theory for one-dimensional Schr\"odinger operators with steplike potentials, which are asymptotically close to different Bohr almost periodic infinite-gap potentials on different half-axes.

In this paper, Morgan type uncertainty principle and unique continuation properties of abstract Schr\"odinger equations with time dependent potentials in vector-valued classes are obtained. The equation involves a possible linear operators…

Singular Gordon potentials are defined to be distributions from the space W^{-1}_{2,unif}(R) that are sufficiently fast approximated by periodic ones. We prove that Schr\"odinger operators with singular Gordon potentials have no point…

We examine two kinds of spectral theoretic situations: First, we recall the case of self-adjoint half-line Schr\"odinger operators on $[a,\infty)$, $a\in\mathbb{R}$, with a regular finite end point $a$ and the case of Schr\"odinger…

We consider Schr\"odinger operators with complex-valued decreasing 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…

Schr\"odinger operators with periodic (possibly complex-valued) potentials and discrete periodic operators (possibly with complex-valued entries) are considered, and in both cases the computational spectral problem is investigated: namely,…

We prove local and global versions of Borg-Marchenko-type uniqueness theorems for half-lattice and full-lattice CMV operators (CMV for Cantero, Moral, and Velazquez) with matrix-valued Verblunsky coefficients. While our half-lattice results…

Here, the Morgan type uncertainty principle and unique continuation properties of abstract Schredinger equations with time dependent potentials are obtained in Hilbert space valued function classes. The equations include linear operator in…

We prove local and global versions of Borg-Marchenko-type uniqueness theorems for half-lattice and full-lattice CMV operators (CMV for Cantero, Moral, and Velazquez \cite{CMV03}). While our half-lattice results are formulated in terms of…

Schr\"odinger operators with potentials generated by primitive substitutions are simple models for one dimensional quasi-crystals. We review recent results on their spectral properties. These include in particular an algorithmically…

Let $\Delta+V$ be the discrete Schr\"odinger operator, where $\Delta$ is the discrete Laplacian on $\mathbb{Z}^d$ and potential $V:\mathbb{Z}^d\to \mathbb{C}$ is $\Gamma$-periodic with $\Gamma=q_1\mathbb{Z}\oplus q_2…

An analogue of Rellich's theorem is proved for discrete Laplacian on square lattice, and applied to show unique continuation property on certain domains as well as non-existence of embedded eigenvalues for discrete Schr{\"o}dinger…

We consider a semi-classical Schr\"odinger operator, -h^2\Delta + V(x). Assuming that the potential admits a unique global minimum and that the eigenvalues of the Hessian are linearly independent over the rationals, we show that the…

We consider non-local Schr\"odinger operators with kinetic terms given by several different types of functions of the Laplacian and potentials decaying to zero at infinity, and derive conditions ruling embedded eigenvalues out. Our goal in…