Optimization and Control Theory Department: 2014-03-11 Nonlinear Seminar

Dr Jacek Gulgowski
(Institute of Mathematics, Gdańsk University)
On the continuity of superposition operator in the spaces of functions of bounded variation

It is a well-know fact that the superposition of a function $f\colon \mathbb{R}\to \mathbb{R}$ satisfying a local Lipschitz condition with a function $x(t)$ of bounded variation leads to the function $(f\circ x)(t)$ which is also of bounded variation. During the seminar we are going to present a few results concerning the continuity of such a superposition operator $F \colon BV[0,1]\to BV[0,1]$ . Furthermore, we are going to discuss several generalizations of the concept of bounded variation in the sense of Jordan and investigate the issue of continuity of the superposition operator $F \colon BV[0,1]\to E$ , where $E$ denotes the space of functions of bounded variation in the generalized sense.