相关论文: Minimal Families of Limit Operators

We consider Schr\"odinger operators on the real line with limit-periodic potentials and show that, generically, the spectrum is a Cantor set of zero Lebesgue measure and all spectral measures are purely singular continuous. Moreover, we…

Let $T:D(T)\rightarrow H_2$ be a densely defined closed operator with domain $D(T)\subset H_1$. We say $T$ to be absolutely minimum attaining if for every closed subspace $M$ of $H_1$, the restriction operator $T|_M:D(T)\cap M\rightarrow…

We investigate the existence or non-existence of spectral minimal partitions of unbounded metric graphs, where the operator applied to each of the partition elements is a Schr\"odinger operator of the form $-\Delta + V$ with suitable…

The purpose of this article is to study pseudospectral properties of the one-dimensional Schr\"{o}dinger operator perturbed by a complex steplike potential. By constructing the resolvent kernel, we show that the pseudospectrum of this…

We consider a family of operators $-\Delta+ t V$ with a slowly decaying and oscillating potential $V$. We prove that the absolutely continuous spectrum of this operator is essentially supported by $[0,\infty)$ for almost every $t$.

We present a brief introduction to the theory of operator limits of random matrices to non-experts. Several open problems and conjectures are given. Connections to statistics, integrable systems, orthogonal polynomials, and more, are…

We consider the spectrum of discrete Schr\"odinger operators with Sturmian potentials and show that for sufficiently large coupling, its Hausdorff dimension and its upper box counting dimension are the same for Lebesgue almost every value…

We consider Schr\"odinger operators on a bounded domain $\Omega\subset \mathbb{R}^3$, with homogeneous Robin or Dirichlet boundary conditions on $\partial\Omega$ and a point (zero-range) interaction placed at an interior point of $\Omega$.…

We consider Dirichlet-to-Neumann maps associated with (not necessarily self-adjoint) Schrodinger operators describing nonlocal interactions in $L^2(\Omega; d^n x)$, $n\geq 2$, where $\Omega$ is an open set with a compact, nonempty boundary…

We study the spectral types of the families of discrete one-dimensional Schr\"odinger operators $\{H_\omega\}_{\omega\in\Omega}$, where the potential of each $H_\omega$ is given by $V_\omega(n)=f(T^n\omega)$ for $n\in\mathbb{Z}$, $T$ is an…

We consider certain parametrised families of piecewise expanding maps on the interval, and estimate and sometimes calculate the Hausdorff dimension of the set of parameters for which the orbit of a fixed point has a certain shrinking target…

We analyze the semiclassical $d$-dimensional Schr\"{o}dinger operator in the continuum $ \frac{1}{2} \Delta + \lambda_N^2 V$ discretized on a mesh with spacing proportional to $1/N$. The semi-classical parameter $\lambda_N$ is chosen as…

We consider a family of multi-dimensional Schr\"odinger operators $-\Delta+t V$ with a real $t$. The potential $V$ in our model decays at infinity in a special way, so that it satisfies a certain integral condition. We prove that the…

We study the microlocal structure of the resolvent of the semi-classical Schrodinger operator with short range potential at an energy which is a unique non-degenerate global maximum of the potential. We prove that it is a semi-classical…

We construct multidimensional Schr\"odinger operators with a spectrum that has no gaps at high energies and that is nowhere dense at low energies. This gives the first example for which this widely expected topological structure of the…

We study how the spectral properties of ergodic Schr\"odinger operators are reflected in the asymptotic properties of its periodic approximation as the period tends to infinity. The first property we address is the asymptotics of the…

The spectral properties of two-dimensional Schr\"odinger operators with $\delta'$-potentials supported on star graphs are discussed. We describe the essential spectrum and give a complete description of situations in which the discrete…

For operators belonging either to a class of global bisingular pseudodifferential operators on $R^m \times R^n$ or to a class of bisingular pseudodifferential operators on a product $M \times N$ of two closed smooth manifolds, we show the…

This paper aims to investigate the pseudo-modes of the one-dimensional Schr\"odinger operator with complex potentials, focusing on the behavior of the resolvent norm along specific curves in the complex plane and assessing the stability of…

Some basic facts about Fredholm indices are briefly reviewed, often used in connection with Toeplitz and pseudodifferential operators, and which may be relevant for operators associated to fractals.