Related papers: Continuum limit for a discrete Hodge-Dirac operato…

We develop a principal trace and generalized index formula for a Dirac-Schr\"odinger operator $D$ on open space of odd dimension $d\geq 3$ with a potential given by a family of self-adjoint unbounded operators acting on a infinite…

In this work, we investigate the discrete Calder\'{o}n problem on grid graphs of dimension three or higher, formed by hypercubic structures. The discrete Calder\'{o}n problem is concerned with determining whether the discrete…

In this paper we study a connection between finite-gap on one energy level two-dimensional Schrodinger operators and two-dimensional discrete operators. We find spectral data for a new class of two-dimensional integrable discrete operators.…

The distance from the identity operator $I$ to $H^*$, the dual of the Hardy averaging operator, is studied on the cone of nonnegative, nonincreasing functions in Lebesgue space. The exact value is obtained. Optimal lower bounds are also…

We discuss the Hardy-Littlewood maximal operator on discrete Morrey spaces of arbitrary dimension. In particular, we obtain its boundedness on the discrete Morrey spaces using a discrete version of the Fefferman-Stein inequality. As a…

Integration over curved manifolds with higher codimension and, separately, discrete variants of continuous operators, have been two important, yet separate themes in harmonic analysis, discrete geometry and analytic number theory research.…

This paper concerns Hodge-Dirac operators D = d + $\delta$ acting in L p ($\Omega$, {\lambda}) where $\Omega$ is a bounded open subset of R n satisfying some kind of Lipschitz condition, {\lambda} is the exterior algebra of R n , d is the…

We investigate the spectrum of the free Neuberger-Dirac operator $\Dov$ on the Schr\"odinger functional (SF). We check that the lowest few eigen-values of the Hermitian operator $\Dov^{\dag}\Dov$ in unit of $L^{-2}$ converge to the…

In this paper we introduce a wide class of space-fractional and time-fractional semidiscrete Dirac operators of L\'evy-Leblond type on the semidiscrete space-time lattice $h\mathbb{Z}^n\times[0,\infty)$ ($h>0$), resembling to fractional…

This paper investigates the $L^p$-boundedness of wave operators associated with the nonhomogeneous fourth-order Sch\"odinger operator $H = \Delta^2 - \Delta + V(x)$ on $\mathbb{R}^n$. Assuming the real-valued potential $ V $ exhibits…

The $\Gamma$-convergence of lower bounded quadratic forms is used to study the singular operator limit of thin tubes (i.e., the vanishing of the cross section diameter) of the Laplace operator with Dirichlet boundary conditions; a procedure…

Formally symmetric differential operators on weighted Hardy-Hilbert spaces are analyzed, along with adjoint pairs of differential operators. Eigenvalue problems for such operators are rather special, but include many of the classical…

The aim of this paper is to construct an explicit potential for the Dirac operator that has purely singular continuous spectrum. The characteristic trait of this potential is that it consists of bumps whose distance is growing rapidly. This…

We derive bounds on the location of non-embedded eigenvalues of Dirac operators on the half-line with non-Hermitian $L^1$-potentials. The results are sharp in the non-relativistic or weak-coupling limit. In the massless case, the absence of…

In this paper, we investigate a class of fractional Hardy type operators $\mathscr{H}_{\beta_{1},\cdots,\beta_{m}}$ defined on higher-dimensional product spaces…

Dimension-free bounds will be provided in maximal and $r$-variational inequalities on $\ell^p(\mathbb Z^d)$ corresponding to the discrete Hardy-Littlewood averaging operators defined over the cubes in $\mathbb Z^d$. We will also construct…

We show that the point spectrum of the standard Coulomb-Dirac operator H_0 is the limit of the point spectrum of the Dirac operator with anomalous magnetic moment H_a as the anomaly parameter tends to 0. For negative angular momentum…

We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can define the notion of order and regularity, and we recover the…

We consider the unperturbed operator $H_0 : = (-i \nabla - A)^2 + W$, self-adjoint in $L^2(\R^2)$. Here $A$ is a magnetic potential which generates a constant magnetic field $b>0$, and the edge potential $W$ is a non-decreasing non constant…

For Schr\"odinger operator $H=-\Delta+ V({\mathbf x})\cdot$, acting in the space $L_2(\mathbb R^d)\,(d\ge 3)$, necessary and sufficient conditions for semi-boundedness and discreteness of its spectrum.are obtained without assumption that…