On the Riesz basis of a family of analytic operators in the sense of Kato and application to the problem of radiation of a vibrating structure in a light fluid

In this paper, we prove that the system formed by some of generalized eigenvectors of the operator T0+εT1+ε2T2+⋯ which are analytic on ε, forms a Riesz basis of the separable Hilbert space H, where ε∈C and T0,T1,T2,… some linear transformations on H which have the same domain D⊆H. After that, we give an application for a problem concerning the radiation of a vibrating structure in a light fluid.