A Banach algebra of functions of several variables of finite total variation and Lipschitzian superposition operators. I
Copyright policy )A Banach algebra of functions of several variables of finite total variation and Lipschitzian superposition operators. I
The author studies the Nemytskij operator \((Hf)(x) = h(x,f(x))\) in the space of functions \(f\) of several variables of bounded variation. In particular, he shows that a Lipschitz condition for \(H\) in the norm of this space leads to a degeneracy of (a certain regularization of) the generating function \(h\). This extends previous results of the author [J. Appl. Anal. 6, No. 2, 173--186 (2000; Zbl 0997.47051); Positivity 5, No. 4, 323--358 (2001; Zbl 1027.47046); J. Math. Sci., New York 111, No. 2, 3387--3429 (2002; Zbl 1033.26014); Nonlinear Anal., Theory Methods Appl. 62, No. 3 (A), 559--578 (2005; Zbl 1083.26011)].
- National Research University Higher School of Economics Russian Federation
- University of Groningen Netherlands
- University High School United States
MAPPINGS, finite total variation, SUBSTITUTION, Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.), Absolutely continuous real functions of several variables, functions of bounded variation, Representation and superposition of functions, Banach algebras of continuous functions, function algebras, COMPOSING FUNCTIONS, Banach algebra property, PRINCIPLE, superposition operator, Lipschitz condition, functions of several variables
MAPPINGS, finite total variation, SUBSTITUTION, Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.), Absolutely continuous real functions of several variables, functions of bounded variation, Representation and superposition of functions, Banach algebras of continuous functions, function algebras, COMPOSING FUNCTIONS, Banach algebra property, PRINCIPLE, superposition operator, Lipschitz condition, functions of several variables
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