Hysteresis filtering in the space of bounded measurable functions

Krejčí, Pavel; Laurençot, Philippe

Bollettino dell'Unione Matematica Italiana, Tome 5-A (2002), p. 755-772 / Harvested from Biblioteca Digitale Italiana di Matematica

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Abstract
Résumé

We define a mapping which with each function $u \in L^{\infty} (0, T)$ and an admissible value of $r > 0$ associates the function $ξ$ with a prescribed initial condition $ξ^{0}$ 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 $ξ^{0}$ , and coincides with the so-called play operator if $u$ is a regulated function.

Si definisce una mappa che associa ad ogni funzione $u \in L^{\infty} (0, T)$ e valore ammissibile $r > 0$ la funzione $ξ$ con condizione iniziale $ξ^{0}$ che minimizza la variazione totale nell' $r$ -intorno di $u$ su ogni sottointervallo $[0, t]$ di $[0, T]$ . Si mostra che questa mappa è non-espansiva rispetto a $u$ , $r$ e $ξ^{0}$ , e che coincide con il cosiddetto operatore play se $u$ è una funzione regolata.

Publié le : 2002-10-01

MR 1934379 | Zbl 1177.35125

@article{BUMI_2002_8_5B_3_755_0,
     author = {Pavel Krej\v c\'\i\ and Philippe Lauren\c cot},
     title = {Hysteresis filtering in the space of bounded measurable functions},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {5-A},
     year = {2002},
     pages = {755-772},
     zbl = {1177.35125},
     mrnumber = {1934379},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2002_8_5B_3_755_0}
}

Krejčí, Pavel; Laurençot, Philippe. Hysteresis filtering in the space of bounded measurable functions. Bollettino dell'Unione Matematica Italiana, Tome 5-A (2002) pp. 755-772. http://gdmltest.u-ga.fr/item/BUMI_2002_8_5B_3_755_0/

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