EIGENVALUES AND EIGEN-FUNCTIONALS OF DIAGONALLY DOMINANT ENDOMORPHISMS IN MIN-MAX ANALYSIS

The so-called (Min, +) analysis may be viewed as an extension to the c ontinuous case and to functional spaces of shortest path algebras in g raphs. We investigate here (Min-Max) analysis which extends, in some s imilar way, minimum spanning tree problems and maximum capacity path p roblems in graphs. An endomorphism A of the functional Min-Max semi-mo dule acts on any functional f to produce Af, where, For All x: [GRAPHI CS] We present here a complete characterization of eigenvalues and eig en-functionals of diagonally dominant endomorphisms (i.e. such that Fo r All x, For All y: A(x, x) = theta(A), A(x,y) greater than or equal t o theta(A)). It is shown, in particular, that any real value lambda > theta(A) is an eigenvalue, and that the associated eigen-semi-module h as a unique minimal generator. (C) 1998 Published by Elsevier Science Inc. All rights reserved.