相关论文: Lyapunov functions for periodic matrix-valued Jaco…

We study the spectral properties of bounded and unbounded Jacobi matrices whose entries are bounded operators on a complex Hilbert space. In particular, we formulate conditions assuring that the spectrum of the studied operators is…

Several examples of Jacobi matrices with an explicitly solvable spectral problem are worked out in detail. In all discussed cases the spectrum is discrete and coincides with the set of zeros of a special function. Moreover, the components…

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…

In this paper we consider the spectrum of the self-adjoint differential operator L generated by the differential expression of order n with the m by m periodic matrix coefficients, where n and m are respectively odd and even integers and…

We introduce the framework of path-complete graph Lyapunov functions for approximation of the joint spectral radius. The approach is based on the analysis of the underlying switched system via inequalities imposed among multiple Lyapunov…

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…

Unlike in complex linear operator theory, polynomials or, more generally, Laurent series in antilinear operators cannot be modelled with complex analysis. There exists a corresponding function space, though, surfacing in spectral mapping…

Koopman operator provides a general linear description of nonlinear systems, whose estimation from data (via extended dynamic mode decomposition) has been extensively studied. However, the elusiveness between the Koopman spectrum and the…

We are interested in diagonal perturbations of a periodic Jacobi operator that introduce embedded eigenvalues in its essential spectrum. Embedding multiple points in the essential spectrum has been known to be difficult, given that…

We consider a periodic Jacobi operator $H$ with finitely supported perturbations on ${\Bbb Z}.$ We solve the inverse resonance problem: we prove that the mapping from finitely supported perturbations to the scattering data: the inverse of…

The Lyapunov spectrum corresponding to a periodic orbit for a two dimensional many particle system with hard core interactions is discussed. Noting that the matrix to describe the tangent space dynamics has the block cyclic structure, the…

Recent results of Denisov and Kaluzhny-Shamis describe the absolutely continuous spectrum of Jacobi matrices with coefficients that obey an l^2 bounded variation condition with step p and are asymptotically periodic. We extend these results…

We consider quasiperiodic Jacobi matrices of size N with analytic coefficients. We show that, in the positive Lyapunov exponent regime, after removing some small sets of energies and frequencies, any eigenvalue is separated from the rest of…

When the coefficients of a Jacobi operator are finitely supported perturbations of the 1 and 0 sequences, respectively, the left reflection coefficient is a rational function whose poles inside, respectively outside, the unit disk…

We investigate spectral properties of the Laplace operator on a class of non-compact Riemannian manifolds. For a given number $N$ we construct periodic (i.e. covering) manifolds such that the essential spectrum of the corresponding…

Consider the Jacobi operators $\cJ$ given by $(\cJ y)_n=a_ny_{n+1}+b_ny_n+a_{n-1}^*y_{n-1}$, $y_n\in \C^m$ (here $y_0=y_{p+1}=0$), where $b_n=b_n^*$ and $a_n:\det a_n\ne 0$ are the sequences of $m\ts m$ matrices, $n=1,..,p$. We study two…

For ergodic 1d Jacobi operators we prove that the random singular components of any spectral measure are almost surely mutually disjoint as long as one restricts to the set of positive Lyapunov exponent. In the context of extended Harper's…

A random phase property is proposed for products of random matrices drawn from any one of the classical groups associated with the ten Cartan symmetry classes of non-interacting disordered Fermion systems. It allows to calculate the…

We study spectral properties of bounded and unbounded complex Jacobi matrices. In particular, we formulate conditions assuring that the spectrum of the studied operators is continuous on some subsets of the complex plane and we provide…

The class of three-diagonal Jacobi matrix with exponentially increasing elements is considered. Under some assumptions the matrix corresponds to unbounded self-adjoint operator in the weighted space. The weight depends on elements of the…