The essential spectrum of a system of singular ordinary differential operators of mixed order. Part I: The general problem and an almost regular case

A system of ordinary differential operators of mixed order on an interval ( 0, r(o)), r(o) > 0, is considered, where the coefficients may be singular a t 0. A special case has been dealt with by KAKO where the essential spectru m of an operator associated with a linearized magnetohydrodynamic equation was explicitly calculated. In the present first:part of:the paper we study an almost regular special case which can be treated by the operator theoret ical methods developed by ATKINSON, LANGER, MENNICKEN and SHKALIKOV. A clos ed linear operator is associated with the given system of differential oper ators and its essential spectrum is explicitly characterized in terms of th e coefficients of these differential operators.