SOME SPECTRAL PROPERTIES FOR THE ASYMPTOTIC-BEHAVIOR OF SEMIGROUPS CONNECTED TO POPULATION-DYNAMICS

This paper gives a short review of the mathematics involved in the study of asymptotic behavior of semigroups arising from structured models of population dynamics. First are considerations on the spectrum of an operator; the main result here is on perturbing the essential spectrum. Then, the spectral theory for a semigroup of operators is reviewed; special attention is paid to positive semigroups. Finally, an example is provided.