Displaying similar documents to “Hysteresis memory preserving operators”

Continuity of hysteresis operators in Sobolev spaces

Pavel Krejčí, Vladimír Lovicar (1990)

Aplikace matematiky

Similarity:

We prove that the classical Prandtl, Ishlinskii and Preisach hysteresis operators are continuous in Sobolev spaces W 1 , p ( 0 , T ) for 1 ≤ p < + ∞ , (localy) Lipschitz continuous in W 1 , 1 ( 0 , T ) and discontinuous in W 1 , ∞ ( 0 , T ) for arbitrary T > 0 . Examples show that this result is optimal.

Uniformly bounded composition operators in the banach space of bounded (p, k)-variation in the sense of Riesz-Popoviciu

Francy Armao, Dorota Głazowska, Sergio Rivas, Jessica Rojas (2013)

Open Mathematics

Similarity:

We prove that if the composition operator F generated by a function f: [a, b] × ℝ → ℝ maps the space of bounded (p, k)-variation in the sense of Riesz-Popoviciu, p ≥ 1, k an integer, denoted by RV(p,k)[a, b], into itself and is uniformly bounded then RV(p,k)[a, b] satisfies the Matkowski condition.