# Extended Perron--Frobenius results

by J.D.Biggins and A. Rahimzadeh Sani

2000 Mathematics Subject Classification: Primary 15A48

## Abstract

Matrices with entries that are smooth functions of a variable $\lambda \in L$ and non-negative when $\lambda \in L_{-}\subset L$ are considered. Perron-Frobenius theory applies when the entries are non-negative. Here, analogous results are shown to hold in neighbourhood of $L_{-}$, with the various quantities varying smoothly. The main examples are matrices with entries that are (i) Fourier-Stieltjes transforms of finite measures and (ii) Laplace-Stieltjes transforms, which arise from Markov-additive processes.

## Availability: Preprint 539/04, Department of Probability and Statistics, University of Sheffield. (September 2003). pdf file or ps file

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