On the essential spectra of coupled operators matrix and application

Abstract

We define an abstract setting to treat essential spectra of unbounded coupled operator matrix. We prove a well-posedness result and develop a spectral theory which also allows us to prove an amelioration to many earlier works. We point out that a concrete example from integro-differential equation fit into this abstract framework involving a general class of regular operator in L 1 spaces. KEYWORDScoupled operator matrix, essential spectra, Fredholm perturbations theory, perfect periodic boundary conditions, transport operator l, w, ss, b}, 7218