Hysteresis filtering in the space of bounded measurable functions
Pavel Krejčı́, Philippe Laurençot · Weierstraß-Institut für Angewandte Analysis und Stochastik · 2000
We define a mapping which with each function u ∈ L∞(0,T) and an admissible value of r > 0 associates the function ξ with a prescribed initial condition ξ0 which minimizes the total variation in the r-neighborhood of u in each subinterval [0,t] of [0,T]. We show that this mapping is non-expansive with respect to u, r and ξ0, and coincides with the so-called play operator if u is a regulated function.