Generalized Riesz basis property in the analysis of neutral type systems

Abstract

International audienceThe functional differential equation of neutral type is studied. We consider the corresponding operator model in Hilbert space M2 = Cn × L2(−1, 0;Cn) and prove that there exists a sequence of invariant finite-dimensional subspaces which constitute a Riesz basis in M2. We also give an example emphasizing that the generalized eigenspaces do not form a Riesz basis