Superposition Operators in the Algebra of Functions of Two Variables with Finite Total Variation
Copyright policy )Superposition Operators in the Algebra of Functions of Two Variables with Finite Total Variation
The author studies the Nemytskij operator \((Hf)(x) = h(x,f(x))\) in the space of functions \(f : [a,b]\times [c,d]\to\mathbb{R}\) of bounded variation. In particular, he shows that a Lipschitz condition for \(H\) in the norm of this space leads to a (mild or strong) degeneracy of the generating function \(h\). This extends previous results of the author [J. Appl. Anal. 6, 173--186 (2000; Zbl 0997.47051), Positivity 5, 323--358 (2001; Zbl 1027.47046), and J. Math. Sci., New York 111, 3387--3429 (2002; Zbl 1033.26014)]{} and by many other authors.
- National Research University Higher School of Economics Russian Federation
- Linguistics University of Nizhny Novgorod Russian Federation
Representation and superposition of functions, finite total variation, Functional equations for real functions, superposition operators, Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.), Absolutely continuous real functions of several variables, functions of bounded variation, functions of two variables, Nemytskij operator
Representation and superposition of functions, finite total variation, Functional equations for real functions, superposition operators, Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.), Absolutely continuous real functions of several variables, functions of bounded variation, functions of two variables, Nemytskij operator
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