On a Riesz basis of eigenvectors of a nonself-adjoint analytic operator and applications.

In the present paper, we deal with the perturbed operatorwhereis a closed densely defined linear operator on a separable Hilbert spaceXwith domainwhileare linear operators onXwith the same domainand satisfying a specific growing inequality. The basic idea here is to investigate under sufficient conditions assuring the existence of a Riesz basis of eigenvectors of the operator. The obtained results are of importance for application to a nonself-adjoint problem describing the radiation of a vibrating structure in a light fluid and to a nonself-adjoint Gribov operator in Bargmann space. [ABSTRACT FROM AUTHOR]