The Play Operator, the Truncated Variation and the Generalisation of the Jordan Decomposition
Classical Analysis and ODEs
2017-06-26 v2
Abstract
The play operator minimalizes the total variation on intervals , of functions approximating uniformly given regulated function with given accuracy and starting from a given point. In this article we link the play operator with so called truncated variation functionals, introduced recently by the second-named author, and provide a semi-explicit expression for the play operator in terms of these functionals. Generalisation for time-dependent boundaries is also considered. This gives the best possible lower bounds for the total variation of the outputs of the play operator and its Jordan-like decomposition.
Keywords
Cite
@article{arxiv.1311.6405,
title = {The Play Operator, the Truncated Variation and the Generalisation of the Jordan Decomposition},
author = {R. Ghomrasni and R. Łochowski},
journal= {arXiv preprint arXiv:1311.6405},
year = {2017}
}