Theory and Numeric of Spectral Value Sets

Abstract

Spectral value sets are useful in studying how the spectrum of closed linear operators on infinite dimensional spaces change under the effect of perturbations. They are also important in investigations related to the transient behaviour of linear systems driven by non-normal operators. In the thesis we show that the spectral value sets that can be achieved by perturbations of a given level can be characterized in terms of the norm of certain transfer function. Furthermore, we present an algorithm able to efficiently calculate these sets in the matrix case. In the general (operator!) case finite dimensional approximations of the corresponding transfer function are the natural approach. Thus, we state the approximation problem and solve it under certain conditions. Finally, we apply our approximation results to the robustness analysis of delay equations and of the Orr-Sommerfeld operator.