Related papers: Resonances for vector-valued Jacobi operators on h…
We study one-dimensional random Jacobi operators corresponding to strictly ergodic dynamical systems. In this context, we characterize the spectrum of these operators by non-uniformity of the transfer matrices and the set where the Lyapunov…
For an arbitrary Hermitian period-$T$ Jacobi operator, we assume a perturbation by a Wigner-von Neumann type potential to devise subordinate solutions to the formal spectral equation for a (possibly infinite) real set, $S$, of the spectral…
We describe a type of n-point function associated to strongly regular vertex operator algebras V and their irreducible modules. Transformation laws with respect to the Jacobi group are developed for 1-point functions. For certain elements…
We show that for a Jacobi operator with coefficients whose (j+1)'th moments are summable the j'th derivative of the scattering matrix is in the Wiener algebra of functions with summable Fourier coefficients. We use this result to improve…
We develop direct and inverse spectral analysis for finite and semi-infinite non-self-adjoint Jacobi matrices with a rank one imaginary part. It is shown that given a set of $n$ not necessarily distinct non-real numbers in the open upper…
We consider semi-infinite Jacobi matrices corresponding to a point interaction for the discrete Schr\"odinger operator. Our goal is to find explicit expressions for the spectral measure, the resolvent and other spectral characteristics of…
We obtain matrix-valued Jost asymptotics for block Jacobi matrices under an L1-type condition on Jacobi parameters, and give a necessary and sufficient condition for an analytic matrix-valued function to be the Jost function of a block…
Spectral properties of Jacobi operators $J$ are intimately related to an asymptotic behavior of the corresponding orthogonal polynomials $P_{n}(z)$ as $n\to\infty$. We study the case where the off-diagonal coefficients $a_{n}$ and,…
We set out to build a framework for self-adjoint extension theory for powers of the Jacobi differential operator that does not make use of classical deficiency elements. Instead, we rely on simpler functions that capture the impact of these…
This paper investigates the spectral properties of Jacobi matrices with limit-periodic coefficients. We show that for a residual set of such matrices, the spectrum is a Cantor set of zero Lebesgue measure, and the spectral measures are…
We apply the methods of classical approximation theory (extreme properties of polynomials) to study the essential support $\Sigma_{ac}$ of the absolutely continuous spectrum of Jacobi matrices. First, we prove an upper bound on the measure…
In this paper, we study the numerical range of Jacobi operators and it is shown that under certain conditions, the boundary of the numerical range of these operators can be non-round only at the points where it touches the essential…
we obtain the asympotics for the counting function of resonances for a matrix valued schrodinger operator in dimension one.
We present a new oscillation criterion to determine whether the number of eigenvalues below the essential spectrum of a given Jacobi operator is finite or not. As an application we show that Kenser's criterion for Jacobi operators follows…
Quasiperiodic Jacobi operators arise as mathematical models of quasicrystals and in more general studies of structures exhibiting aperiodic order. The spectra of these self-adjoint operators can be quite exotic, such as Cantor sets, and…
We prove that the resolvent set of any, possibly singular, quasi periodic Jacobi operator is characterized as the set of all energies whose associated Jacobi cocycles induce a dominated splitting. This extends a well-known result by R. A.…
This paper is the continuation of the study on discrete harmonic analysis related to Jacobi expansions initiated in [1]. Considering the operator $\mathcal{J}^{(\alpha,\beta)}=J^{(\alpha,\beta)}-I$, where $J^{(\alpha,\beta)}$ is the…
We study spectrum inclusion regions for complex Jacobi matrices which are compact perturbations of real periodic Jacobi matrices. The condition sufficient for the lack of discrete spectrum for such matrices is given
We consider resonances for third order ordinary differential operator with compactly supported coefficients on the real line. Resonance are defined as zeros of a Fredholm determinant on a non-physical sheet of three sheeted Riemann surface.…
We investigate dynamics of Josephson vortex lattice in layered high T$_{c}$ superconductors at high magnetic fields. It is shown that the average electric current depends on the lattice structure and is resonantly enhanced when the…