Abstract
Abstract This paper studies a linear hyperbolic system with boundary conditions that was first studied under some weaker conditions in [8, 11]. Problems on the expansion of a semigroup and a criterion for being a Riesz basis are discussed in the present paper. It is shown that the associated linear system is the infinitesimal generator of a C 0 {C_{0}} -semigroup; its spectrum consists of zeros of a sine-type function, and its exponential system { e λ n t } n ≥ 1 {\{e^{\lambda_{n}t}\}_{n\geq 1}} constitutes a Riesz basis in L 2 [ 0 , T ] {L^{2}[0,T]} . Furthermore, by the spectral analysis method, it is also shown that the linear system has a sequence of eigenvectors, which form a Riesz basis in Hilbert space, and hence the spectrum-determined growth condition is deduced.
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