WIAS Preprint No. 608, (2000)

Hysteresis filtering in the space of bounded measurable functions


  • Krejčí, Pavel
    ORCID: 0000-0002-7579-6002
  • 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.

Appeared in

  • Bollettino U. M. I. (8) 5-B (2002), pp. 755-772

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