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arXiv · 1311.6405

The Play Operator, the Truncated Variation and the Generalisation of the Jordan Decomposition

R. Ghomrasni·R. Łochowski
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Abstract

The play operator minimalizes the total variation on intervals $[0,T], T> 0$, 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.

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R. Ghomrasni, R. Łochowski. 2015-03-06. The Play Operator, the Truncated Variation and the Generalisation of the Jordan Decomposition. https://doi.org/10.1002/mma.3077

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