Riesz Basis Property of Families of Nonharmonic Exponentials and Application to a Problem of a Radiation of a Vibrating Structure in a Light Fluid
Salma Charfi, Aref Jeribi, Ines Walha · Numerical Functional Analysis and Optimization · 2011
This article deals with the Riesz basis property of families of nonharmonic exponentials. The exponents coincide with the eigenvalues of a specific perturbation of a closed linear operator. The key idea of this work is based on the estimate given by Nagy [6 B. Sz. Nagy , ( 1951 ). Perturbations des transformations linéaires fermées . Comment. Math. Helv. 125 – 137 . [Google Scholar]] using the spectral analysis method. Furthermore, it is also shown that the system of a sequence of exponentials families of the operator forms a Riesz basis in L 2(0, T), T > 0, where K is the integral operator with kernel the Hankel function of the first kind and order 0.