The paper shows that the global exponential stability property is preserved, under suitably fast sampling and small input-delay, whenever the dynamics of the time-delay system at hand and the related stabilizing (in continuous-time) state feedback are described by globally Lipschitz maps. The Halanay’s inequality is used in order to prove this result. Continuous-time, possibly non-affine in the...

The notion of gradient flows is generalized to a metric space setting without any linear structure. The metric spaces considered are a generalization of Hilbert spaces, and the properties of such metric spaces are used to set up a finite-difference scheme of variational form. The proof of the Crandall–Liggett generation theorem is adapted to show convergence. The resulting flow generates a stro...

Based on the notion Minimizing Lipschitz Extensions and its connection with the infinity Laplacian, a computational framework for surface warping and in particular brain warping (the nonlinear registration of brain imaging data) is presented in this paper. The basic concept is to compute a map between surfaces that minimizes a distortion measure based on geodesic distances while respecting the ...

Let 0 ≤ α < 1. Denote the open unit polydisk in C by ∆. We obtain a purely function-theoretic condition characterizing the holomorphic self-maps of ∆ that induce bounded composition operators on (1−α)-Bloch spaces, which we define on ∆. As a consequence, we extend Madigan’s characterization of bounded composition operators on analytic α-Lipschitz spaces over ∆ for 0 < α < 1 to an analogous char...

In this paper we demonstrate that a number of fixed point iteration problems can be solved using a modified Krasnoselskij iteration process, which is much simpler to use than the other iteration schemes that have been defined. 2008 Elsevier Inc. All rights reserved. For maps with a slow enough growth rate, the Banach contraction principle provides the existence and uniqueness of the fixed point...

We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.