Hysteresis filtering in the space of bounded measurable functions
- Krejčí, Pavel
- Laurençot, Philippe
2010 Mathematics Subject Classification
- 34C55 26A45
- hysteresis, play operator, total variation
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.
- Bollettino U. M. I. (8) 5-B (2002), pp. 755-772