Hysteresis memory preserving operators

Pavel Krejčí

Displaying similar documents to “Hysteresis memory preserving operators”

Hysteresis operators - a new approach to evolution differential inequalities

Pavel Krejčí (1989)

Commentationes Mathematicae Universitatis Carolinae

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Continuity of hysteresis operators in Sobolev spaces

Pavel Krejčí, Vladimír Lovicar (1990)

Aplikace matematiky

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

Lipschitz functions with unexpectedly large sets of nondifferentiability points.

Csörnyei, Marianna, Preiss, David, Tišer, Jaroslav (2005)

Abstract and Applied Analysis

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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

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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.