Related papers: A quantitative Borg-Levinson theorem for a large c…
The first author established in [8] a quantitative Borg-Levinson theorem for the Schr\"odinger operator with unbounded potential. In the present work, we extend the results in [8] to the magnetic Schr\"odinger operator. We discuss both the…
We establish the Borg-Levinson theorem for elliptic operators of higher order with constant coefficients. The case of incomplete spectral data is also considered.
We deduce Levinson\'{}s theorem in non-relativistic quantum mechanics in one dimension as a sum rule for the spectral density constructed from asymptotic data. We assume a self-adjoint hamiltonian which guarantees completeness; the…
This text deals with multidimensional Borg-Levinson inverse theory. Its main purpose is to establish that the Dirichlet eigenvalues and Neumann boundary data of the Dirichlet Laplacian acting in a bounded domain of dimension 2 or greater,…
A two-dimensional analogue of Levinson's theorem for nonrelativistic quantum mechanics is established, which relates the phase shift at threshold(zero momentum) for the $m$th partial wave to the total number of bound states with angular…
The two-dimensional Levinson theorem for the Klein-Gordon equation with a cylindrically symmetric potential $V(r)$ is established. It is shown that $N_{m}\pi=\pi (n_{m}^{+}-n_{m}^{-})= [\delta_{m}(M)+\beta_{1}]-[\delta_{m}(-M)+\beta_{2}]$,…
In this article, we prove a quantitative version of Carleson's $\varepsilon^2$ conjecture in higher dimension: we characterise those Ahlfors-David regular domains in $\mathbb{R}^{n+1}$ for which the Carleson's coefficients satisfy the…
We show that there exists $c>0$ such that any subset of $\{1, \dots, N\}$ of density at least $(\log\log{N})^{-c}$ contains a nontrivial progression of the form $x,x+y,x+y^2$. This is the first quantitatively effective version of the…
We consider the Poisson Boolean continuum percolation model in n-dimensional hyperbolic space. In 2 dimensions we show that there are intensities for the underlying Poisson process for which there are infinitely unbounded components in the…
We study the potential theory of a large class of infinite dimensional L\'evy processes, including Brownian motion on abstract Wiener spaces. The key result is the construction of compact Lyapunov functions, i.e. excessive functions with…
We provide a Kingman-like Theorem for arbitrary finite measures and a version of Birkhoff's Theorem for bounded observable. As an application, we show that Birkhoff's limit exists for some continuous observable, in an example of Bowen.
In this note, we prove an $L^2$ Hartogs-type extension theorem for unbounded domains.
Gromov and Piatetski-Shapiro proved existence of finite volume non-arithmetic hyperbolic manifolds of any given dimension. In dimension four and higher, we show that there are about v^v such manifolds of volume at most v, considered up to…
Suppose that G is a finite group and A is a subset of G such that 1_A has algebra norm at most M. Then 1_A is a plus/minus sum of at most L cosets of subgroups of G, and L can be taken to be triply tower in O(M). This is a quantitative…
We apply an inductive argument to three theorems of Cantor on (1) the uncountability of infinite binary sequences, (2) the uncountability of real numbers, and (3) the non-equinumerosity of sets with their powersets. This technique proves…
We define and examine nonlinear potential by Bessel convolution with Bessel kernel. We investigate removable sets with respect to Laplace-Bessel inequality. By studying the maximal and fractional maximal measure, a Wolff type inequality is…
Numerous properties of vector addition systems with states amount to checking the (un)boundedness of some selective feature (e.g., number of reversals, run length). Some of these features can be checked in exponential space by using…
We give an overview of recent results on Lieb-Robinson bounds and some of their applications in the study of quantum many-body models in condensed matter physics.
This paper extends the tools of C*-algebraic strict quantization toward analyzing the classical limits of unbounded quantities in quantum theories. We introduce the approach first in the simple case of finite systems. Then we apply this…
We prove that the Dirichlet eigenvalues and Neumann boundary data of the corresponding eigenfunctions of the operator $-\Delta + q$, determine the potential $q$, when $q \in L^{n/2}(\Omega,\mathbb{R})$ and $n \geq 3$. We also consider the…