Related papers: On the zero modes of Pauli operators

For $\nu\in[0, 1]$ let $D^\nu$ be the distinguished self-adjoint realisation of the three-dimensional Coulomb-Dirac operator $-\mathrm i\boldsymbol\alpha\cdot\nabla -\nu|\cdot|^{-1}$. For $\nu\in[0, 1)$ we prove the lower bound of the form…

Consider the elliptic operator \[ A = - \sum_{k,l=1}^d \partial_k \, c_{kl} \, \partial_l + \sum_{k=1}^d a_k \, \partial_k - \sum_{k=1}^d \partial_k \, b_k + a_0 \] on a bounded connected open set $\Omega \subset {\bf R}^d$ with Lipschitz…

We prove that the Bergman kernel of the symmetrized polydisc in dimension greater than two has zeros.

This article describes a class of pseudo-differential operators \begin{equation*} (\mathcal{A}^{\alpha}\varphi)(x)=\mathcal{F}^{-1}_{\xi \rightarrow…

For $1<p<\infty$ we prove an $L^p$-version of the generalized trace-free Korn inequality for incompatible tensor fields $P$ in $ W^{1,\,p}_0(\operatorname{Curl}; \Omega,\mathbb{R}^{3\times3})$. More precisely, let…

We consider Fock spaces $F^{p,\ell}_{\alpha}$ of entire functions on ${\mathbb C}$ associated to the weights $e^{-\alpha |z|^{2\ell}}$, where $\alpha>0$ and $\ell$ is a positive integer. We compute explicitly the corresponding Bergman…

Let $\Omega$ be a bounded convex Reinhardt domain in $\mathbb{C}^2$ and $\phi\in C(\bar{\Omega})$. We show that the Hankel operator $H_{\phi}$ is compact if and only if $\phi$ is holomorphic along every non-trivial analytic disc in the…

We define for arbitrary modules over a finite von Neumann algebra $\cala$ a dimension taking values in $[0,\infty]$ which extends the classical notion of von Neumann dimension for finitely generated projective $\cala$-modules and inherits…

We consider $L$-$\omega$-nonexpansive maps $T\colon K\to K$ on a convex subset $K$ of a Banach space $X$, i.e., maps in which $\omega_T(\delta)\leq L\delta +\omega(\delta)$ with $L\in [0,1]$, $\omega$ being a modulus of continuity and…

Let $\mathcal{G}^{(\lambda)}$ be a group scheme which deforms $\mathbb{G}_a$ to $\mathbb{G}_m$. We explicitly describe the Cartier dual of the $l$-th Frobenius type kernel $N_l$ of the group scheme $\mathcal{E}^{(\lambda,\mu;D)}$ which is…

The paper provides two versions of nonlocal Poincar\'e-type inequalities for integral operators with a convolution-type structure and functions satisfying a zero-Dirichlet like condition. The inequalities extend existing results to a large…

Recently, Liang and Partington \cite{YP} show that kernels of finite-rank perturbations of Toeplitz operators are nearly invariant with finite defect under the backward shift operator acting on the scalar-valued Hardy space. In this article…

The method of quantization of magnetic monopoles based on the order-disorder duality existing between the monopole operator and the lagrangian fields is applied to the description of the quantum magnetic monopoles of `t Hooft and Polyakov…

Toeplitz plus Hankel operators $T(a)+H(b)$, $a,b\in L^\infty$ acting on the classical Hardy spaces $H^p, 1<p<\infty$, are studied. If the generating functions $a$ and $b$ satisfy the so-called matching condition $a(t) a(1/t)=b(t) b(1/t)$,…

This paper is devoted to semiclassical estimates of the eigenvalues of the Pauli operator on a bounded open set whose boundary carries Dirichlet conditions. Assuming that the magnetic field is positive and a few generic conditions, we…

For an open subset $\Omega$ of $\mathbb R^d$, symmetric with respect to a hyperplane and with positive part $\Omega_+$, we consider the Neumann/Dirichlet Laplacians $-\Delta_{N/D,\Omega}$ and $-\Delta_{N/D,\Omega_+}$. Given a Borel function…

Let $\T (0\leq \alpha <n)$ be the singular and fractional integrals with variable kernel $\Omega(x,z)$, and $[b,\T]$ be the commutator generated by $\T$ and a Lipschitz function $b$. In this paper, the authors study the boundedness of…

In a bounded domain $G$ with smooth border studied boundary value and spectral problems for operators of the rotor (vortex) and the gradient of the divergence $+\lambda\,I$ in the Sobolev spaces. For $\lambda\neq 0$ these operators are…

We characterize the non-atomic measures $\mu$ for which all Calder\'{o}n-Zygmund operators with antisymmetric kernels of a fixed non-integer dimension $s$ are bounded in $L^2(\mu)$ in terms of a positive quantity, the Wolff energy.

This paper is devoted to wavelet analysis on adele ring $\bA$ and the theory of pseudo-differential operators. We develop the technique which gives the possibility to generalize finite-dimensional results of wavelet analysis to the case of…