SOME REMARKS ON THE ESSENTIAL SPECTRUM OF TRANSPORT OPERATORS WITH ABSTRACT BOUNDARY-CONDITIONS

This article deals with the analysis of the essential spectrum of the one-dimensional transport operator with general boundary conditions wh ere an abstract boundary operator relates the incoming and the outgoin g fluxes. After a complete description of the spectrum of the transpor t equation with vacuum boundary conditions, sufficient conditions are given in terms of boundary and collision operators assuring the stabil ity of the essential spectrum. The article ends with an analysis of th e essential spectrum of the neutron transport operator in arbitrary di mension. Finally, some open problems are indicated.