Abstract
In this paper, we are interested by the perturbed operator $$\begin{aligned} T(\varepsilon ):=T_0+\varepsilon T_1 +\varepsilon ^2T_2+\cdots +\varepsilon ^k T_k+\cdots \end{aligned}$$ where $$\varepsilon \in \mathbb {C}$$ , $$T_0$$ is a closed densely defined linear operator on a separable Hilbert space $$\mathcal{H}$$ with domain $$\mathcal{D}(T_0)$$ having isolated eigenvalues with multiplicity one whereas $$T_1, T_2,\ldots $$ are linear operators on $$\mathcal{H}$$ having the same domain $$\mathcal{D}\supset \mathcal{D}(T_0)$$ and satisfying a specific growing inequality. The basic idea here is to investigate under sufficient conditions the existence of Riesz bases of exponentials, where the exponents corresponding as a sequence of eigenvalues of $$T(\varepsilon )$$ , can be developed as entire series of $$\varepsilon $$ . An application to a nonself-adjoint problem describing the radiation of a vibrating structure in a light fluid is presented.
Published Version
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