An inversion formula for a Prandtl-Ishlinskii operator with time dependent thresholds

We extend the well-known inversion result for Prandtl-Ishlinskii operators to the case of time dependent thresholds. The exact inversion formula is shown to hold under the condition that the distances between the thresholds do not decrease in time. Examples show that this threshold dilation condition cannot be completely omitted. (C) 2011 Elsevier B.V. All rights reserved.