Upper bounds on wavepacket spreading for random Jacobi matrices

Dynamical Upper Bounds on Wavepacket Spreading

Lower bounds of Copson type for the transpose of matrices on weighted sequence spaces

Upper and lower bounds for numerical radii of block shifts

For an n-by-n complex matrix A in a block form with the (possibly) nonzero blocks only on the diagonal above the main one, we consider two other matrices whose nonzero entries are along the diagonal above the main one and consist of the norms or minimum moduli of the diagonal blocks of A. In this paper, we obtain two inequalities relating the numeical radii of these matrices and also determine ...

Upper Bounds for Quantum Dynamics Governed by Jacobi Matrices with Self-similar Spectra

We study a class of one-sided Hamiltonian operators with spectral measures given by invariant and ergodic measures of dynamical systems of the interval. We analyse dimensional properties of spectral measures, and prove upper bounds for the asymptotic spread in time of wavepackets. These bounds involve the Hausdorr dimension of the spectral measure, multiplied by a correction calculated from the...

Sharp Bounds on the PI Spectral Radius

In this paper some upper and lower bounds for the greatest eigenvalues of the PI and vertex PI matrices of a graph G are obtained. Those graphs for which these bounds are best possible are characterized.