Related papers: On an application of generalized Jentzsch theorem …

In J. Math. Anal. App. 305. (2005), we have considered the Gribov operator\\ $H_{\lambda'} = \lambda' S + H_{\mu,\lambda}$ acting on Bargmann space where $ S = a^{*2} a^{2}$ and $ H_{\mu,\lambda} =\mu a^* a + \\i \lambda a^* (a+a^*)a$ with…

In 1998, we have given in ([14] Intissar, A., Analyse de Scattering d'un op\'erateur cubique de Heun dans l'espace de Bargmann, Comm.Math.Phys.199 (1998) 243-256) the boundary conditions at infinity for a description of all maximal…

We consider families of tridiagonal- matrices with diagonal $\beta_{k} = \mu k$ and off-diagonal entries $\alpha_{k} = i\lambda k\sqrt{k+1}$; $1 \leq k \leq n$, $n \in \mathbb{N}$ and $i^{2} = -1$ where $\mu \in \mathbb{C}$ and $\lambda \in…

In this article, we obtain a regularized trace formula for magic Gribov operator\\ $ H = \lambda{''}G + H_{\mu,\lambda}$ acting on Bargmann space where $$G = a^{*3}a^{3} \quad \quad and \quad \quad H_{\mu,\lambda} = \mu a^{*}a + i\lambda…

A new representation -which is similar to the Bargmann representation- of the creation and annihilation operators is introduced, in which the operators act like "multiplication with" and like "derivation with respect to" a single real…

Let $\Omega$ be a subdomain of $\mathbb{C}$ and let $\mu$ be a positive Borel measure on $\Omega$. In this paper, we study the asymptotic behavior of the eigenvalues of compact Toeplitz operator $T_\mu$ acting on Bergman spaces on $\Omega$.…

Let $H$ be a Schr\"odinger operator defined on a noncompact Riemannian manifold $\Omega$, and let $W\in L^\infty(\Omega;\mathbb{R})$. Suppose that the operator $H+W$ is critical in $\Omega$, and let $\varphi$ be the corresponding Agmon…

Let $\mathcal{H}=-\Delta_{\mathbb{H}}+V$ be the Schr\"odinger operator on the Heisenberg group $\mathbb{H}^n$, where $\Delta_{\mathbb{H}}$ is the full laplacian on $\mathbb{H}^n$ and $V$ is a positive smooth potential, bounded below and…

A model operator $H_\mu,$ $\mu>0$ associated to a system of three particles on the three-dimensional lattice $ \mathbb{Z}^3$ that interact via nonlocal pair potentials is considered. We study the case where the parameter function $w$ has a…

Let $\sigma(A)$, $\rho(A)$ and $r(A)$ denote the spectrum, spectral radius and numerical radius of a bounded linear operator $A$ on a Hilbert space $H$, respectively. We show that a linear operator $A$ satisfying $$\rho(AB)\le r(A)r(B)…

We study the spectral bounds of self-adjoint operators on the Hilbert space of square-integrable functions, arising from the representation theory of the Heisenberg group. Interestingly, starting either with the von Neumann lattice or the…

The Hamiltonian reggeon acting in Bargmann space is non-Hermitian with respect to the standard scalar product associated to Bargmann space. Hence the question arises, whether the eigenfunctions by the finite norm condition form a complete…

HVZ type theorem for semi-relativistic Pauli-Fierz Hamiltonian, $$\HHH=\sqrt{(p\otimes \one -A)^2+M^2}+V\otimes \one +\one\otimes \hf,\quad M\geq 0,$$ in quantum electrodynamics is studied. Here $H$ is a self-adjoint operator in Hilbert…

We study numerically the so-called fundamental modular region Lambda, a region free of Gribov copies, in the minimal Landau gauge for pure SU(2) lattice gauge theory. To this end we evaluate the influence of Gribov copies on several…

We consider a self-adjoint two-dimensional Schr\"odinger operator $H_{\alpha\mu}$, which corresponds to the formal differential expression \[ -\Delta - \alpha\mu, \] where $\mu$ is a finite compactly supported positive Radon measure on…

Let $\mu$ be a positive Borel measure on the interval [0,1). For $\beta > 0$, The generalized Hankel matrix $\mathcal{H}_{\mu,\beta}= (\mu_{n,k,\beta})_{n,k\geq0}$ with entries $\mu_{n,k,\beta}=…

We consider one dimensional Schr\"{o}dinger operators $H_\lambda=-\frac{d^2}{dx^2}+U+ \lambda V_\lambda$ with nonlinear dependence on the parameter $\lambda$ and study the small $\lambda$ behaviour of eigenvalues. The potentials $U$ and…

We study a class of Schr\"odinger operators $H_{m,\lambda}$ with generalized Thue-Morse potential that generated by the substitution $\tau(a)=a^mb^m$, $\tau(b)=b^ma^m$ on two symbol alphabet $\Sigma=\{a,b\}$ for integer $m\ge 2$ and…

Let $\mathcal{M}$ be a semifinite von Neumann algebra on a Hilbert space $\mathcal{H}$ equipped with a faithful normal semifinite trace $\tau$, $S(\mathcal{M},\tau)$ be the ${}^*$-algebra of all $\tau$-measurable operators. Let…

In the Kaluza - Klein approach the (4+d)-dimensional Einstein--Hilbert gravity action is considered. The extra d-dimensional manifold V_d is a Riemann space with the d-parametric group of isometry $G_d$ which acts on V_d by the left shifts…