Related papers: Remarks on Periodic Jacobi Matrices on Trees

In this research we obtain the classical r-matrices of real two and three dimensional Jacobi-Lie bialgebras. In this way, we classify all non-isomorphic real two and three dimensional coboundary Jacobi-Lie bialgebras and their types…

In this paper, we establish two types of upper bounds on the vanishing order of Jacobi forms at infinity. The first type is for classical Jacobi forms, which is optimal in a certain sense. The second type is for Jacobi forms of lattice…

We investigate the differential equation for the Jacobi-type polynomials which are orthogonal on the interval $[-1,1]$ with respect to the classical Jacobi measure and an additional point mass at one endpoint. This scale of higher-order…

The higher rank numerical ranges of generic matrices are described in terms of the components of their Kippenhahn curves. Cases of tridiagonal (in particular, reciprocal) 2-periodic matrices are treated in more detail.

We consider the Jacobi matrix generated by a balanced measure of hyperbolic polynomial map. The conjecture of Bellissard says that this matrix should have an extremely strong periodicity property. We show how this conjecture is related to a…

We introduce a quantitative condition on orbits of dynamical systems which measures their aperiodicity. We show the existence of sequences in the Bernoulli-shift and geodesics on closed hyperbolic manifolds which are as aperiodic as…

In general, point spectrum of an almost periodic Jacobi matrix can depend on the element of the hull. In this paper, we study the hull of the limit-periodic Jacobi matrix corresponding to the equilibrium measure of the Julia set of the…

In this paper we study a class of Jacobi operators, such that each operator is generated by the unit Borel measure with a support consisting of a finite number of intervals on the real line R and a finite number of points in C, located…

This paper provides decay bounds for Green matrices and generalized eigenvectors of block Jacobi operators when the real part of the spectral parameter lies in a bounded gap of the operator's essential spectrum. The case of the spectral…

A Jacobi matrix with matrix entries is a self-adjoint block tridiagonal matrix with invertible blocks on the off-diagonals. The Weyl surface describing the dependence of Green's matrix on the boundary conditions is interpreted as the set of…

We characterize the spectrum of one-dimensional Jacobi operators H=aS^{+}+a^{-}S^{-}+b in l^{2}(\Z) with quasi-periodic complex-valued algebro-geometric coefficients (which satisfy one (and hence infinitely many) equation(s) of the…

We consider two-sided Jacobi matrices whose coefficients are obtained by continuous sampling along the orbits of a homeomorphim of a compact metric space. Given an ergodic probability measure, we study the topological structure of the…

A method is presented for proving upper bounds on the moments of the position operator when the dynamics of quantum wavepackets is governed by a random (possibly correlated) Jacobi matrix. As an application, one obtains sharp upper bounds…

We give upper and lower bounds on the number of points on abelian varieties over finite fields, and lower bounds specific to Jacobian varieties. We also determine exact formulas for the maximum and minimum number of points on Jacobian…

Naturally reductive spaces, in general, can be seen as an adequate generalization of Riemannian symmetric spaces. Nevertheless, there are some that are closer to symmetric spaces than others. On the one hand, there is the series of Hopf…

We study periodic monopoles satisfying some mild conditions, called of GCK type. Particularly, we give a classification of periodic monopoles of GCK type in terms of difference modules with parabolic structure, which is a kind of…

Periodic Jacobi operators naturally arise in numerous applications, forming a cornerstone in various fields. The spectral theory associated with these operators boasts an extensive body of literature. Considered as discretized counterparts…

The Randic (connectivity) index is one of the most successful molecular descriptors in structure-property and structure-activity relationships studies. J. Gao found the sharp upper bound for the Randic index of apex trees. In this paper, we…

The study of solutions with fixed energy of certain classes of Lagrangian (or Hamiltonian) systems is reduced, via the classical Maupertuis--Jacobi variational principle, to the study of geodesics in Riemannian manifolds. We are interested…

In this paper we prove that the existence of absolutely continuous spectrum of the Kirchhoff Laplacian on a radial metric tree graph together with a finite complexity of the geometry of the tree implies that the tree is in fact eventually…