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

Abstract

In this paper, we prove that the system formed by some of generalized eigenvectors of the operator T 0 + εT 1 + ε 2 T 2 + · · · which are analytic on ε, forms a Riesz basis of the separable Hilbert space H, where ε ∈ C and T 0 , T 1 , T 2 , . . . 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.

On an unconditional basis of generalized eigenvectors of an analytic operator and application to a problem of radiation of a vibrating structure in a light fluid

“…In the present paper, we deal with the operator T (ε) := T 0 + εT 1 + ε 2 T 2 + · · · + ε k T k + · · · (see [3,4,11]), verifying the following conditions:…”