Riesz Basis Property of Evolution Equations in Hilbert Spaces and Application to a Coupled String Equation

Suppose that \λ ₙ\ is the set of zeros of a sine-type generating function of the exponential system λₙ t\ in L 2 (0,T) and is separated. Levin and Golovin's classical theorem claims that λₙ t\ forms a Riesz basis for L 2 (0,T). In this article, we relate this result with Riesz basis generation of eigenvectors of the system operator of the linear time-invariant evolution equation in Hilbert spaces through its spectrum. A practically favorable necessary and sufficient condition for the separability of zeros of function of sine type is derived. The result is applied to get Riesz basis generation of a coupled string equation with joint dissipative feedback control.