On a General Feshbach Method1

Abstract

We present a general reduction Feshbach method that can be applied in particular to the spectral study of operators including the hamiltonian of the Born-Oppenheimer approximation and also to Fredholm operators. This method reduces the study on the first case to the one of a pseudodifferential matrix, and in the second case to a matrix acting between two finite dimensional euclidian spaces. The stability theorem of the Fredholm character and the index is originally obtained as a consequence of this reduction.