Related papers: On the zero modes of Pauli operators

We consider the asymptotic properties of the eigenvalues of the Neumann-Poincare (NP) operator in three dimensions. The region $\Omega\subset \mathbb{R}^3$ is bounded by a compact surface $\Gamma=\partial \Omega$, with certain smoothness…

The paper treats pseudodifferential operators $P=Op(p(\xi ))$ with homogeneous complex symbol $p(\xi )$ of order $2a>0$, generalizing the fractional Laplacian $(-\Delta )^a$ but lacking its symmetries, and taken to act on the halfspace…

Every closed subspace of each of the Banach spaces $X = \ell_p(\Gamma)$ and $X=c_0(\Gamma)$, where $\Gamma$ is a set and $1<p<\infty$, is the kernel of a bounded operator $X\to X$. On the other hand, whenever $\Gamma$ is an uncountable set,…

In this paper we study the kernels of Toeplitz operators on both the scalar and the vector-valued Hardy space for $ 1 < p < \infty $. We show existence of a minimal kernel of any element of the vector-valued Hardy space and we determine a…

We prove, under certain conditions, the existence of zeros for a weakly continuous operator on a paracompact topological space into the dual of a Banach space.

The paper analyses the decay of any zero modes that might exist for a massless Dirac operator $H:= \ba \cdot (1/i) \bgrad + Q, $ where $Q$ is $4 \times 4$-matrix-valued and of order $O(|\x|^{-1})$ at infinity. The approach is based on…

It is a result by Lacey and Thiele that the bilinear Hilbert transform maps L^{p_1}(R) \times L^{p_2}(R) into L^{p_3}(R) whenever (p_1,p_2,p_3) is a Holder tuple with p_1,p_2 > 1 and p_3>2/3. We study the behavior of the quartile operator,…

We consider degenerate differential operators $A = \displaystyle{\sum_{k,j=1}^d \partial_k (a_{kj} \partial_j)}$ on $L^2(\mathbb{R}^d)$ with real symmetric bounded measurable coefficients. Given a function $\chi \in…

Based on the Mehler heat kernel of the Schroedinger operator for a free electron in a constant magnetic field an estimate for the kernel of E_A is derived, where E_A represents the kinetic energy of a Dirac electron within the…

The polarization operator is investigated at arbitrary photon energy in a constant and homogeneous magnetic field for the strength H less than the Schwinger critical value. The effective mass of a real photon with a preset polarization is…

We consider kernels of discrete convolution operators or, equivalently, homogeneous solutions of partial difference operators and show that these solutions always have to be exponential polynomials. The respective polynomial space in…

For a singular measure $\mu$, Ahlfors regular of order $\alpha>0,$ with compact support in $\mathbb{R}^{\mathbf{N}}$ and a pseudodifferential operator $\mathbf{A}$ of order $-l=-\mathbf{N}/2$ we consider the compact operator…

Recently, it was shown that the image of a Toeplitz kernel of dimension greater than $1$ under composition by an inner function is nearly $S^*$-invariant if and only if the inner function is an automorphism. Building on this, we determine…

In this short technical note, we extend a recently published result [Liao2017] on the Perron root (or the spectral radius) of non-negative matrices to real-valued non-negative kernels on an arbitrary measurable space $(\mathrm{E},…

It is shown that a self-dual neutral Einstein four-manifold of Petrov type III, admitting a two-dimensional null parallel distribution compatible with the orientation, cannot be compact or locally homogeneous, and its maximum possible…

Given a self-adjoint operator $T$ on a separable infinite-dimensional Hilbert space we study the problem of characterizing the set $\mathcal D(T)$ of all possible diagonals of $T$. For compact operators $T$, we give a complete…

In this short note, as a simple application of the strong result proved recently by B\"ohm and Wilking, we give a classification on closed manifolds with 2-nonnegative curvature operator. Moreover, by the new invariant cone constructions of…

Assume that $\Omega_{1}$ and $\Omega_{2}$ are two smooth bounded pseudoconvex domains in $\mathbb{C}^{2}$ that intersect (real) transversely, and that $\Omega_{1} \cap \Omega_{2}$ is a domain (i.e. is connected). If the…

We consider the Dirichlet Pauli operator in bounded connected domains in the plane, with a semi-classical parameter. We show, in particular, that the ground state energy of this Pauli operator will be exponentially small as the…

For $n$-normal operators $A$ [2, 4, 5], equivalently $n$-th roots $A$ of normal Hilbert space operators, both $A$ and $A^*$ satisfy the Bishop--Eschmeier--Putinar property $(\beta)_{\epsilon}$, $A$ is decomposable and the quasi-nilpotent…