Approximation invariance of semi-group operators under perturbations

Group invariance and L-bounded operators

In this paper we consider translation invariant operators with additional symmetry coming from group actions. As the classic Hilbert and Riesz transforms can be characterized up to scalar by means of relative invariance of conformal transformation groups, certain multiplier operators are characterized by relative invariance of some other affine subgroups. In this article, we formalize a geometr...

Invariance of the Approximately Reachable Set under Nonlinear Perturbations

This paper considers nonlinear perturbations of control systems with linear dynamics and seeks to analyze whether the approximately reachable set may be left unchanged by this perturbation. Under suitable conditions it is shown that this analysis may be reduced to the presumably simpler analysis of such invariance for a family of affine perturbations. Interest centers on the context of infinite...

The Behavior of Functions of Operators under Perturbations

This is a survey article. We consider different problems in connection with the behavior of functions of operators under perturbations of operators. We deal with three classes of operators: unitary operators, self-adjoint operators, and contractions. We study operator Lipschitz and operator differentiable functions. We also study the behavior of functions under perturbations of an operator by a...

Perturbations of Operators, Ii

Semi-Infinite Optimization under Convex Function Perturbations: Lipschitz Stability

This paper is devoted to the study of the stability of the solution map for the parametric convex semi-infinite optimization problem under convex function perturbations in short, PCSI. We establish sufficient conditions for the pseudo-Lipschitz property of the solution map of PCSI under perturbations of both objective function and constraint set. The main result obtained is new even when the pr...