Hysteresis filtering in the space of bounded measurable functions

Krejčí, Pavel, and Laurençot, Philippe. "Hysteresis filtering in the space of bounded measurable functions." Bollettino dell'Unione Matematica Italiana 5-B.3 (2002): 755-772. <http://eudml.org/doc/195526>.

@article{Krejčí2002,
abstract = {We define a mapping which with each function $u\in L^\{\infty\}(0, T)$ and an admissible value of $r > 0$ associates the function $\xi$ with a prescribed initial condition $\xi^\{0\}$ 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 $\xi^\{0\}$, and coincides with the so-called play operator if $u$ is a regulated function.},
author = {Krejčí, Pavel, Laurençot, Philippe},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {755-772},
publisher = {Unione Matematica Italiana},
title = {Hysteresis filtering in the space of bounded measurable functions},
url = {http://eudml.org/doc/195526},
volume = {5-B},
year = {2002},
}

TY - JOUR
AU - Krejčí, Pavel
AU - Laurençot, Philippe
TI - Hysteresis filtering in the space of bounded measurable functions
JO - Bollettino dell'Unione Matematica Italiana
DA - 2002/10//
PB - Unione Matematica Italiana
VL - 5-B
IS - 3
SP - 755
EP - 772
AB - We define a mapping which with each function $u\in L^{\infty}(0, T)$ and an admissible value of $r > 0$ associates the function $\xi$ with a prescribed initial condition $\xi^{0}$ 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 $\xi^{0}$, and coincides with the so-called play operator if $u$ is a regulated function.
LA - eng
UR - http://eudml.org/doc/195526
ER -