Restrictions of Normal Operators, Padé Approximation and Autoregressive Time Series

Abstract

This work studies restrictions of normal operators on a Hilbert space to so-called Krylov subspaces with special attention to selfadjoint and unitary operators. It is shown that the characteristic polynomials of these restrictions are orthogonal polynomials and furthermore are intimately related to denominators of Padé approximations to certain moment generating functions. These relations are seen to unify certain aspects of Lanczos methods for eigenvalue approximations of selfadjoint operators and autoregressive modeling of time series.