Related papers: A magnetic eigenvalue bound in the disk

We derive novel guaranteed lower bounds for eigenvalues of the Euler-Bernoulli beam with variable bending stiffness. While the standard finite element Rayleigh-Ritz method automatically yields upper bounds, we obtain lower bounds by…

The object of the present study is the integrated density of states of a quantum particle in multi-dimensional Euclidean space which is characterized by a Schr\"odinger operator with a constant magnetic field and a random potential which…

This paper is concerned with the estimation of the number of negative eigenvalues (bound states) of Schroedinger operators in a strip subject to Neumann boundary conditions. The estimates involve weighted L^1 norms and L ln L norms of the…

This article is concerned with uniqueness and stability issues for the inverse spectral problem of recovering the magnetic field and the electric potential in a Riemannian manifold from some asymptotic knowledge of the boundary spectral…

We consider a magnetic Schr\"odinger operator $(\nabla^X)^*\nabla^X+q$ on a compact Riemann surface with boundary and prove a $\log\log$-type stability estimate in terms of Cauchy data for the electric potential and magnetic field under the…

Lieb has shown a lower bound on the smallest Dirichlet eigenvalue of the Laplace operator in terms of a generalized inradius. We derive similar bounds for Robin eigenvalues, for eigenvalues of the polyharmonic operator and the sub-Laplacian…

Let $\Omega\subset\mathbb{R}^N$, $N\geq 1$, be an open bounded connected set. We consider the indefinite weighted eigenvalue problem $-\Delta u =\lambda m u$ in $\Omega$ with $\lambda \in \mathbb{R}$, $m\in L^\infty(\Omega)$ and with…

We consider a two dimensional magnetic Schroedinger operator with a spatially stationary random magnetic field. We assume that the magnetic field has a positive lower bound and that it has Fourier modes on arbitrarily short scales. We prove…

In this study we investigate the bound states of the Hamiltonian describing a quantum particle living on three dimensional straight strip of width $d$. We impose the Neumann boundary condition on a disc window of radius $a$ and Dirichlet…

There have been, over the last 8 years, a number of far reaching extensions of the famous original F. and M. Riesz's uniqueness theorem that states that if a bounded analytic function in the unit disc of the complex plane $\Bbb C$ has the…

A local Tb Theorem provides a flexible framework for proving the boundedness of a Calder\'on-Zygmund operator T. One needs only boundedness of the operator T on systems of locally pseudo-accretive functions \{b_Q\}, indexed by cubes. We…

This paper gives a framework to produce the lower bound of eigenvalues defined in a Hilbert space by the eigenvalues defined in another Hilbert space. The method is based on using the max-min principle for the eigenvalue problems.

Consider a closed curve of length $2\pi$ with curvature $\kappa(s)$ and the Schr\"odinger operator $H$ with $\kappa^2$ as the potential term. Let $\lambda_\Gamma$ be the lowest eigenvalue of $H$. The Ovals Conjecture proposed by Benguria…

We prove an inequality with applications to solutions of the Schr\"odinger equation. There is a universal constant $c>0$, such that if $\Omega \subset \mathbb{R}^2$ is simply connected, $u:\Omega \rightarrow \mathbb{R}$ vanishes on the…

We study Poincar\'e-Wirtinger type inequalities in the framework of magnetic fractional Sobolev spaces. In the local case, Lieb-Seiringer-Yngvason [E. Lieb, R. Seiringer, and J. Yngvason, Poincar\'e inequalities in punctured domains, Ann.…

In this article, we establish a geometric lower bound for the first positive eigenvalue $\lambda^{(1)}_{1}$ of the rough Laplacian acting on $1$-forms for closed $2n$-dimensional Riemannian manifolds with nonvanishing Euler characteristic.…

We prove that the eigenvalues $\lambda_n(c)$ of the time-frequency localization operator satisfy $\lambda_n(c) > 1 - \delta^c$ for $n = [(1-\varepsilon)c]$, where $\delta = \delta(\varepsilon) < 1$ and $\varepsilon > 0$ is arbitrary,…

Let $\Omega$ be a smooth bounded domain in $\mathbf R^2$ and $\lambda^{\mathsf N} (\Omega)$ the first non-zero Neumann eigenvalue of the operator $-\Delta$ on $\Omega$. In this paper, for any $\gamma \in [0, \lambda^{\mathsf N} (\Omega) )$,…

The celebrated conjecture by Payne, P\'{o}lya and Weinberger (1956) states that for the fixed membrane problem, the ratio of the first two eigenvalues, $\lambda_2/\lambda_1$, is maximized by a disk. A more general dimensional version of…

Given a constant magnetic field on Euclidean space ${\mathbb R}^p$ determined by a skew-symmetric $(p\times p)$ matrix $\Theta$, and a ${\mathbb Z}^p$-invariant probability measure $\mu$ on the disorder set $\Sigma$ which is by hypothesis a…