Frame of Exponentials Related to Analytic Families Operators and Application to a Non-self Adjoint Problem of Radiation of a Vibrating Structure in a Light Fluid

Abstract

In the present paper, we investigate under sufficient conditions the existence of frames of exponential families, where the exponents coincide with the eigenvalues of the perturbed operatorHere T 0 is a closed densely defined linear operator on a separable Hilbert space H with domain D(T 0 ) having isolated eigenvalues with multiplicity one and T 1 , T 2 , . . . are linear operators on H having the same domain D ⊃ D(T 0 ) and satisfying a specific growing inequality. The obtained results are applied to a non-self adjoint problem deduced from a perturbation method for sound radiation.