Fredholm properties of a class of coupled operator matrices and their applications.

This paper deals with Fredholm properties of the one-sided coupled operator matrix M = A B 0 D I 0 L I by means of generalized Schur factorization and the associated space decompositions. For λ ∈ C , some sufficient conditions are given for λ - M to be Fredholm (resp. left or right Fredholm), and these conclusions are further used to determine the essential spectra of a delay equation and a wave equation with acoustic boundary conditions. [ABSTRACT FROM AUTHOR]