COMPLETENESS OF ROOT FUNCTIONS FOR THERMAL CONDUCTION IN A STRIP AND A SECTOR

In singularity theory, the solution of the problem is frequently expre ssed as a function of eigenvectors of the operator obtained by separat ion of variables. However when the medium is heterogeneous, the operat or is not symmetric. The eigenvalues may be defective i.e. associated with Jordan block. Without showing that the system of root functions i s a basis, we shall prove in this Note that for stationary thermal con duction in a strip or a sector, the system is complete.