Riesz basis generation of discrete operators and application to a linear thermoelastic system

Abstract

In this paper, we give a new result of Riesz basis generation property for discrete operators in Hilbert spaces, from which, we show that the generalized eigenfunctions of a one-dimensional linear thermoelastic system with Dirichlet-Dirichlet boundary condition form a Riesz basis in the state Hilbert space. This develops a parallel result which is already known for the same systems with Dirichlet-Neumann or Neumann-Dirichlet boundary conditions [S.W.Hansen, J.Math.Anal.Appl., 167(1992), 429-442].