Related papers: Central spectral gaps of the almost Mathieu operat…

Katugampola's 2015 study of generalized fractional differential operators produced triangular arrays of integer coefficients indexed by a fractional order r and by dimensions n and k, but no combinatorial interpretation has been established…

In this work the method of analyzing of the absolutely continuous spectrum for self-adjoint operators is considered. For the analysis it is used an approximation of self-adjoint operator $A$ by a sequence of operators $A_n$ with absolutely…

In this paper we study the $\nu$-continuity of the spectrum and some of its parts. We show that the approximate point spectrum $\sigma_{ap}$ is upper semi-$\nu$-continuous at every Fredholm operator, then we give sufficient conditions to…

We consider a non-Hermitian medium with a gain and loss symmetric, exponentially damped potential distribution to demonstrate different scattering features analytically. The condition for critical coupling (CC) for unidirectional wave and…

Let $M$ be a connected, noncompact, complete Riemannian manifold, consider the operator $L=\DD +\nn V$ for some $V\in C^2(M)$ with $\exp[V]$ integrable w.r.t. the Riemannian volume element. This paper studies the existence of the spectral…

Spectral singularities are spectral points that spoil the completeness of the eigenfunctions of certain non-Hermitian Hamiltonian operators. We identify spectral singularities of complex scattering potentials with the real energies at which…

We examine the band-gap structure of the spectrum of the Neumann problem for the Laplace operator in a strip with periodic dense transversal perforation by identical holes of a small diameter $\varepsilon>0$. The periodicity cell itself…

In this paper we consider critical points of the following nonlocal energy {equation} {\cal{L}}_n(u)=\int_{\R^n}| ({-\Delta})^{n/4} u(x)|^2 dx\,, {equation} where $u\colon H^{n/2}(\R^n)\to{\cal{N}}\,$ ${\cal{N}}\subset\R^m$ is a compact $k$…

Let $\Omega\subset\mathbb{R}^3$ be an open set, we study the spectral properties of the free Dirac operator $\mathcal{H}$ coupled with the singular potential $V_\kappa=(\epsilon I_4 +\mu\beta+\eta(\alpha\cdot N))\delta_{\partial\Omega}$.…

We present results on the broadband nature of the power spectrum $S(\omega)$, $\omega\in(0,2\pi)$, for a large class of nonuniformly expanding maps with summable and nonsummable decay of correlations. In particular, we consider a class of…

We introduce a unitary almost-Mathieu operator, which is obtained from a two-dimensional quantum walk in a uniform magnetic field. We exhibit a version of Aubry--Andr\'{e} duality for this model, which partitions the parameter space into…

Consider a quasi-periodic Schr\"odinger operator $H_{\alpha,\theta}$ with analytic potential and irrational frequency $\alpha$. Given any rational approximating $\alpha$, let $S_+$ and $S_-$ denote the union, respectively, the intersection…

We provide a simplified proof of the existence, under some assumptions, of a spectral gap for the Perron-Frobenius operator of piecewise uniformly expanding maps on Riemannian manifolds when acting on some Sobolev spaces. Its consequences…

Let $\alpha\in \mathbb{R}\backslash \mathbb{Q}$ and $\beta(\alpha) = \limsup _{n \to \infty}(\ln q_{n+1})/ q_n <\infty$, where $p_n/q_n$ is the continued fraction approximations to $\alpha$. Let $(H_{\lambda,\alpha,\theta}u)…

A model operator $H$ corresponding to a three-particle discrete Schr\"odinger operator on a lattice $\Z^3$ is studied. The essential spectrum is described via the spectrum of two Friedrichs models with parameters $h_\alpha(p),$…

The nearest-neighbor Aubry-Andr\'e quasiperiodic localization model is generalized to include power-law translation-invariant hoppings $T_l\propto t/l^a$ or power-law Fourier coefficients $W_m \propto w/m^b$ in the quasi-periodic potential.…

It is well known from the Perron-Frobenius theory that the spectral gap of a positive square matrix is positive. In this paper, we give a more quantitative characterization of the spectral gap. More specifically, using a complex extension…

We give general spectral and eigenvalue perturbation bounds for a selfadjoint operator perturbed in the sense of the pseudo-Friedrichs extension. We also give several generalisations of the aforementioned extension. The spectral bounds for…

We study the semigroup of the symmetric $\alpha$-stable process in bounded domains in $\R^2$. We obtain a variational formula for the spectral gap, i.e. the difference between two first eigenvalues of the generator of this semigroup. This…

We show that the spectral gap of a random walk on the domain of normal attraction of an $\alpha$-stable law is of order $\mathcal O(n^{\alpha})$ when restricted to boxes of size $n$. The proof is based on a comparison principle that may be…