STABILITY AND RIESZ BASIS PROPERTY FOR GENERAL NETWORK OF STRINGS

摘要

In this paper, we study the generation problem of Riesz basis for a general network of strings with joint damping at each vertex. First, we give a basic spectral property of the system operator A. Under certain conditions, we prove that the spectrum of A is distributed in a strip parallel to the imaginary axis. By the discussion of the completeness of generalized eigenvectors of the operator A, we prove further that there exists a sequence of generalized eigenvectors of A that forms a Riesz basis with parentheses in the Hilbert state space.