Related papers: The Maxwell operator with periodic coefficients in…
The article surveys the main techniques and results of the spectral theory of periodic operators arising in mathematical physics and other areas. Close attention is paid to studying analytic properties of Bloch and Fermi varieties, which…
For families of magnetic self-adjoint operators on ${\mathbb Z}^d$ whose symbols and magnetic fields depend continuously on a parameter $\epsilon$, it is shown that the main spectral properties of these operators also vary continuously with…
In this article, we give conditions guaranteeing the commutativity of a bounded self-adjoint operator with an unbounded closed symmetric operator.
We consider a Schr\"odinger operator $H=-\Delta+V(\vec x)$ in dimension two with a quasi-periodic potential $V(\vec x)$. We prove that the absolutely continuous spectrum of $H$ contains a semiaxis and there is a family of generalized…
It is known that the Lyapunov exponent of analytic 1-frequency quasiperiodic cocycles is continuous in cocycle and, when the frequency is irrational, jointly in cocycle and frequency. In this paper, we extend a result of Bourgain to show…
This paper contributes to the analysis of the peripheral (point) spectrum of positive linear operators on Banach lattices. We show that, under appropriate growth and regularity conditions, the peripheral point spectrum of a positive…
This article presents a mathematical framework for solving Maxwell's equations in cylindrical and spherical geometries with continuous angular indices. We extend beyond standard discrete harmonic decomposition to a continuous spectral…
We prove that the massless Dirac operator in $\mathbb{R^3}$ with long-range potential has an a.c. spectrum which fills the whole real line. The Dirac operators with matrix-valued potentials are considered as well.
The absolutely continuous spectrum of one-dimensional Schr\"odinger operators is proved to be stable under perturbation by potentials satisfying mild decay conditions. In particular, the absolutely continuous spectrum of free and periodic…
In this paper, for d > 2, we prove the absolute continuity of the spectrum of a d-dimensional periodic Dirac operator with some discontinuous magnetic and electric potentials. In particular, for d = 3, electric potentials from Zygmund…
We prove new criteria of stability of the absolutely continuous spectrum of one-dimensional Schr\"odinger operators under slowly decaying perturbations. As applications, we show that the absolutely continuous spectrum of the free and…
We consider Schr\"odinger operators with periodic electric and magnetic potentials on periodic discrete graphs. The spectrum of such operators consists of an absolutely continuous (a.c.) part (a union of a finite number of non-degenerate…
We study spectrum of the periodic coupling AMO model. Meantime there establish the continuity of Lyapunov exponent about the the periodic coupling of AMO model. Through the dynamical method can find a interval the AMO model only have…
A practical solution for the mathematical problem of functional calculus with Laplace-Beltrami operator on surfaces with axial symmetry is found. A quantitative analysis of the spectrum is presented.
In this paper we characterize mixing composition operators acting on the space $\mathscr{O}_M(\mathbb{R})$ of slowly increasing smooth functions. Moreover we relate the mixing property of those operators with the solvability of Abel's…
We study resolvent estimate and maximal regularity of the Stokes operator in $L^q$-spaces with exponential weights in the axial directions of unbounded cylinders of ${\mathbb R}^n,n\geq 3$. For straights cylinders we obtain these results in…
We treat some questions related to supercyclicity of continuous linear operators when acting in locally convex spaces. We extend results of Ansari and Bourdon and consider doubly power bounded operators in this general setting. Some…
We carry out expansions of non-symmetric toroidal ideal magnetohydrodynamic (MHD) equilibria with nested flux surfaces about a periodic cylinder, in which physical quantities are periodic of period $2\pi$ in the cylindrical angle $\theta$…
We consider transverse propagation of electromagnetic waves through a two-dimensional composite material containing a periodic rectangular array of circular cylinders. Propagation of waves is described by the Helmholtz equation with the…
In this paper we study the existence of periodic orbits in the flow of non-singular steady Euler fields $X$ on closed 3-manifolds, that is $X$ is a solution of time independent Euler equations. We show, that when $X$ is $C^2$ the flow…