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Positive Semigroups: I. The finite-dimensional case.

MACSI at the department of Mathematics and Statistics at the University of Limerick invites you to a seminar

Speaker:                     Dr. Eberhard Mayerhofer (Department of Mathematics and Statistics, University of Limerick)

Time & location:       Friday 12th October, at 4p.m.  Room A2-002

Title:                           Positive Semigroups: I. The finite-dimensional case.

Abstract: I construct linear (!) norm-like functions on cones, which generate Lyapunov maps on their duals. Using multivariate comparison arguments for ODEs, we characterize generators of positive (cone-valued) linear semigroups on cones and their resolvents and understands their spectral bound as the largest eigenvalue. The main statement allows to test linear maps for strictly negative spectral bound. Applications lie in ODE theory (stability, e.g. for Matrix Riccati Differential equations) and the theory of high-dimensional Markov processes on cones (geometric ergodicity). Our theory recovers well known results for M and Z matrices as well.

The presentation addresses anybody with interest in Linear Algebra.

If you have any questions regarding this seminar, please direct them to Romina Gaburro (061 2131930, email  and Clifford Nolan (061 202766),

Supported by Science Foundation Ireland funding, MACSI - the Mathematics Applications Consortium for Science and Industry (, centred at the University of Limerick, is dedicated to the mathematical modelling and solution of problems which arise in science, engineering and industry in Ireland.