Archivio Istituzionale della RicercaThe most natural and important topologies connected with hysteresis operators are those induced by uniform convergence, W1,1-convergence, and strict convergence. Indeed the supremum norm and the variation are invariant under reparameterization. We prove a general result that implies that if a hysteresis operator is continuous with respect to the topology of W1,1, then it is continuous with respect to the strict topology.
Sobolev and strict continuity of general hysteresis operators / Recupero, Vincenzo. - In: MATHEMATICAL METHODS IN THE APPLIED SCIENCES. - ISSN 0170-4214. - 32:(2009), pp. 2003-2018. [10.1002/mma.1124]
Sobolev and strict continuity of general hysteresis operators
RECUPERO, VINCENZO
2009
Abstract
The most natural and important topologies connected with hysteresis operators are those induced by uniform convergence, W1,1-convergence, and strict convergence. Indeed the supremum norm and the variation are invariant under reparameterization. We prove a general result that implies that if a hysteresis operator is continuous with respect to the topology of W1,1, then it is continuous with respect to the strict topology.
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https://hdl.handle.net/11583/1875400
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