Related papers: Spectral approximation of aperiodic Schr\"odinger …

A periodic Schr\"odinger operator on a noncompact Riemannian manifold $M$ such that $H^1(M, \mathbb R)=0$ endowed with a properly discontinuous cocompact isometric action of a discrete group is considered. Under some additional conditions…

The quaternionic spectral theorem has already been considered in the literature, see e.g. [22], [31], [32], however, except for the finite dimensional case in which the notion of spectrum is associated to an eigenvalue problem, see [21], it…

We consider in a Hilbert space a self-adjoint operator H and a family Phi=(Phi_1,...,Phi_d) of mutually commuting self-adjoint operators. Under some regularity properties of H with respect to Phi, we propose two new formulae for a time…

The behavior of the discrete spectrum of the Schr\"odinger operator $-\D - V$, in quite a general setting, up to a large extent is determined by the behavior of the corresponding heat kernel $P(t;x,y)$ as $t\to 0$ and $t\to\infty$. If this…

We exhibit limit-periodic Schr\"odinger operators that are uniformly localized in the strongest sense possible. That is, for these operators there are uniform exponential decay rates such that every element of the hull has a complete set of…

The paper contains a brief description of a simplified version of A. Sobolev's proof of absolute continuity of spectra of periodic magnetic Schr\"{o}dinger operators. This approach is applicable to all periodic elliptic operators known to…

We consider Schr\^odinger operators $H_\alpha$ given by equation (1.1) below. We study the asymptotic behavior of the spectral density $E(H_\alpha, \lambda)$ when $\lambda$ goes to $0$ and the $L^1\to L^\infty$ dispersive estimates…

We prove sufficient conditions for Hausdorff convergence of the spectra of sequences of closed operators defined on varying Hilbert spaces and converging in norm-resolvent sense, i.e. $\|J_\varepsilon(1+A_\varepsilon)^{-1} -…

This paper deals with the approximation of a magnetic Schr\"odinger operator with a singular $\delta$-potential that is formally given by $(i \nabla + A)^2 + Q + \alpha \delta_\Sigma$ by Schr\"odinger operators with regular potentials in…

We consider the discrete eigenvalues of the operator $H_\eps=-\Delta+V(\x)+\eps^2Q(\eps\x)$, where $V(\x)$ is periodic and $Q(\y)$ is localized on $\R^d,\ \ d\ge1$. For $\eps>0$ and sufficiently small, discrete eigenvalues may bifurcate…

The spectral analysis of discretized one-dimensional Schr\"{o}dinger operators is a very difficult problem which has been studied by numerous mathematicians. A natural problem at the interface of numerical analysis and operator theory is…

We investigate the effect of non-symmetric relatively bounded perturbations on the spectrum of self-adjoint operators. In particular, we establish stability theorems for one or infinitely many spectral gaps along with corresponding…

It is proven that the absolutely continuous spectrum of matrix Schr\"{o}dinger operators coincides (with the multiplicity taken into account) with the spectrum of the unperturbed operator if the (matrix) potential is square integrable. The…

In this note it is proved that the complete spectral data of selfadjoint Schr\"odinger operators on unbounded domains can be described with an associated Dirichlet-to-Neumann map. In particular, a characterization of the isolated and…

We consider continuous $SL(2,\mathbb{R})$-cocycles over a strictly ergodic homeomorphism which fibers over an almost periodic dynamical system (generalized skew-shifts). We prove that any cocycle which is not uniformly hyperbolic can be…

Assume that $T_1,T_2$ are equivalent Schauder operators. In this paper, we show that even in this case their Schauder spectrum may be very different in the view of operator theory. In fact, we get that if a self-adjoint Schauder operator…

We study the operators in the large $N$ tensor models, focusing mostly on the fermionic quantum mechanics with $O(N)^3$ symmetry which may be either global or gauged. In the model with global symmetry we study the spectra of bilinear…

In \cite{Lee:2006:schrod-converg}, when the spatial variable $x$ is localized, Lee observed that the Schr\"odinger maximal operator $e^{it\Delta}f(x)$ enjoys certain localization property in $t$ for frequency localized functions. In this…

We look at invariance of a.e. boundary condition spectral behavior under perturbations, $W$, of half-line, continuum or discrete Schr\"odinger operators. We extend the results of del Rio, Simon, Stolz from compactly supported $W$'s to…

We study spectra of Schr\"odinger operators on $\RR^d$. First we consider a pair of operators which differ by a compactly supported potential, as well as the corresponding semigroups. We prove almost exponential decay of the singular values…