相关论文: Riesz bases consisting of root functions of 1D Dir…

In this paper, we obtain two Lichnerowicz type formulas for the Dirac-Witten operators. And we give the proof of Kastler-Kalau-Walze type theorems for the Dirac-Witten operators on 4-dimensional and 6- dimensional compact manifolds with…

Given a domain D in R^d with mild geometric measure theoretic assumptions on its boundary, we show that boundedness of the principal value Riesz tranforms (witn kernel of homogeneity -(d-1)) on H\"older spaces of order alpha on the boundary…

In this paper we explore some basic properties of quasi-Banach function spaces which are important in applications. Namely, we show that they posses a generalised version of Riesz--Fischer property, that embeddings between them are always…

We consider \textit{additive spaces}, consisting of two intervals of unit length or two general probability measures on ${\mathbb R}^1$, positioned on the axes in ${\mathbb R}^2$, with a natural additive measure $\rho$. We study the…

We extend the theory of operator-valued frames (resp. bases), hence the theory of frames (resp. bases), for Hilbert spaces and Hilbert C*-modules, in two folds. This extension leads us to develop the theory of operator-valued frames (resp.…

The Dirac equation is considered in the background of potentials of several types, namely scalar and vector-potentials as well as "Dirac-oscillator" potential or some of its generalisations. We investigate the radial Dirac equation within a…

The exact solutions of the (2+1) dimensional Dirac equation on the torus and the new extension and generalization of the trigonometric Poschl-Teller potential families in terms of the torus parameters are obtained. Supersymmetric quantum…

We obtain inequalities for the Riesz means for the discrete spectrum of a class of self-adjoint compact integral operators. Such bounds imply some inequalities for the counting function of the Dirichlet boundary problem for the Laplace…

We study the behavior of the spectrum of the Dirac operator on degenerating families of compact Riemannian surfaces, when the length $t$ of a simple closed geodesic shrinks to zero, under the hypothesis that the spin structure along the…

Let $D$ be a connected bounded domain in $\R^2$, $S$ be its boundary which is closed, connected and smooth. Let $\Phi(z)=\frac 1 {2\pi i}\int_S\frac{f(s)ds}{s-z}$, $f\in L^1(S)$, $z=x+iy$. Boundary values of $\Phi(z)$ on $S$ are studied.…

Let $C_h$ be a composition operator mapping $L^2(\Omega_1)$ into $L^2(\Omega_2)$ for some open sets $\Omega_1, \Omega_2 \subseteq \mathbb{R}^n$. We characterize the mappings $h$ that transform Riesz bases of $L^2(\Omega_1)$ into Riesz bases…

We shall say that a bounded linear operator $T$ acting on a Banach space $X$ admits a generalized Kato-Riesz decomposition if there exists a pair of $T$-invariant closed subspaces $(M,N)$ such that $X=M\oplus N$, the reduction $T_M$ is Kato…

We examine the threshold of the cyclicity for functions in Dirichlet-type spaces $\mathcal{D}_{\alpha}$, $\alpha\in(0,1]$. Given a fixed $\alpha^{*}\in(0,1]$, we construct a holomorphic function $f\in\mathcal{D}_{\alpha^{*}}$ which is…

Aldroubi has shown how one can construct any frame $\gtu$ starting with one frame $\ftu $,using a bounded operator $U$ on $l^2(N)$. We study the overcompleteness of the frames in terms of properties of $U$. We also discuss perturbation of…

We obtain and analyze equations determining first-order differential symmetry operators with matrix coefficients for the Dirac equation with an external electromagnetic potential in a $(2+1)$-dimensional Riemann (curved) spacetime.…

We establish the regularity theory for certain critical elliptic systems with an anti-symmetric structure under inhomogeneous Neumann and Dirichlet boundary constraints. As applications, we prove full regularity and smooth estimates at the…

We study sub-Dirac operators that are associated with left-invariant bracket-generating sub-Riemannian structures on compact quotients of nilpotent semi-direct products $G=\mathbb{R}^n\rtimes_A\mathbb{R}$. We will prove that these operators…

In this article we obtain the asymptotic formulas for the eigenvalues and eigenfunctions of the nonself-adjoint operator generated by a system of Sturm-Liouville equations with summable coefficients and the quasiperiodic boundary…

Let $E\subset \mathbb{R}^{n+1}$, $n\ge 2$, be a closed, Ahlfors-David regular set of dimension $n$ satisfying the "Riesz Transform bound" $$\sup_{\varepsilon>0}\int_E\left|\int_{\{y\in E:|x-y|>\varepsilon\}}\frac{x-y}{|x-y|^{n+1}} f(y)…

Despite the recent advances in the theory of exponential Riesz bases, it is yet unknown whether there exists a set $S \subset \mathbb{R}^d$ which does not admit a Riesz spectrum, meaning that for every $\Lambda \subset \mathbb{R}^d$ the set…