1305.7208 (Oleg Szehr)

Eigenvalue estimates for the resolvent of a non-normal matrix    [PDF]

Oleg Szehr

We derive spectral estimates on the norm of the resolvent for two classes of matrices. First, we consider matrices, whose largest singular value is bounded by 1. We recover and generalize the estimates obtained by E.B. Davies and B. Simon for such matrices. In the second part we improve known upper bounds on the resolvent of a power-bounded matrix. To achieve our estimates we take a function space based approach building on the techniques developed by N. Nikolski. Finally, we apply our results to study the sensitivity of the stationary states of a classical or quantum Markov chain to perturbations of the transition matrix.

View original: http://arxiv.org/abs/1305.7208