TY - JOUR
T1 - Extension of hysteresis operators of Preisach-type to real, Lebesgue measurable functions
AU - Iyer, R.
AU - Ekanayake, D.
PY - 2008/2/1
Y1 - 2008/2/1
N2 - Functions in Llocp [0, ∞) where 1 ≤ p ≤ ∞ can be considered as inputs to linear systems. However, hysteresis operators of Preisach type have only been defined on much smaller space of regulated (or Baire) functions. In this paper, we re-define Play operators so that they are well defined for real valued measurable functions. We show that this definition coincides with the older definition for continuous and regulated functions on an interval. Domain extension of hysteresis operators of Preisach type to real, Lebesgue measurable functions is then obtained in the standard manner using the re-defined Play operators.
AB - Functions in Llocp [0, ∞) where 1 ≤ p ≤ ∞ can be considered as inputs to linear systems. However, hysteresis operators of Preisach type have only been defined on much smaller space of regulated (or Baire) functions. In this paper, we re-define Play operators so that they are well defined for real valued measurable functions. We show that this definition coincides with the older definition for continuous and regulated functions on an interval. Domain extension of hysteresis operators of Preisach type to real, Lebesgue measurable functions is then obtained in the standard manner using the re-defined Play operators.
KW - Hysteresis operators of Preisach type
KW - Lebesgue measurable functions
UR - http://www.scopus.com/inward/record.url?scp=37349057424&partnerID=8YFLogxK
U2 - 10.1016/j.physb.2007.08.069
DO - 10.1016/j.physb.2007.08.069
M3 - Article
AN - SCOPUS:37349057424
SN - 0921-4526
VL - 403
SP - 437
EP - 439
JO - Physica B: Condensed Matter
JF - Physica B: Condensed Matter
IS - 2-3
ER -