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Nonlinear Superposition Operators
1990This book is a self-contained account of knowledge of the theory of nonlinear superposition operators: a generalization of the notion of functions. The theory developed here is applicable to operators in a wide variety of function spaces, and it is here that the modern theory diverges from classical nonlinear analysis.
Jürgen Appell, Petr P. Zabrejko
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Superposition Operators on Bloch-Type Spaces
Computational Methods and Function Theory, 2007The article deals with the superposition operator \(S_\varphi(f)(z) = \varphi(f(z))\) between the Bloch-type spaces \({\mathcal B}^\alpha\), \(0 < \alpha < \infty\), of all analytic functions \(f(z)\) on the unit disk satisfying \[ \| f\| _{{\mathcal B}^\alpha} = | f(0)| + \sup_{| z| < 1}(1 - | z| ^2)^\alpha \, | f'(z)| < \infty \] (\({\mathcal B ...
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Superposition of Substitution Operators
1967The present section forms a bridge leading to the second part of our material — integral operators. There is no implication that integral operators in general (or even Integral operators of any particular type) have to be introduced as superposition of substitution operators.
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Superposition operators, -universal functions, and the hyperbolic composition operator
Acta Mathematica Hungarica, 2012We give a description of those functions f in the unit ball Open image in new window of H∞ on the disk \(\mathbb{D}\) whose orbit {f∘ϕn: n∈ℕ} is locally uniformly dense in Open image in new window for some sequence (ϕn) of selfmaps of \(\mathbb{D}\). An interpretation of this result in terms of the superposition (or substitution) operator on the space ...
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Superposition operators between logarithmic Bloch spaces
Rendiconti del Circolo Matematico di Palermo Series 2, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Malavé-Malavé, Renny J. +1 more
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The superposition operator in Orlicz spaces
1990Whenever one has to deal with problems involving rapidly increasing nonlinearities (e.g. of exponential type), Orlicz spaces are more appropriate than Lebesgue spaces. Since Orlicz spaces are ideal spaces, many statements of this section are just reformulations of the general results of Chapter 2, and therefore are cited mostly without proofs. However,
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Modular metric spaces, II: Application to superposition operators
Nonlinear Analysis: Theory, Methods & Applications, 2010The author presents an exhausting description of Lipschitz continuous and some other classes of nonlinear superposition operators acting in modular metric spaces of functions of a real variable of finite generalized variation in the sense of \textit{M. Schramm} [Trans. Am. Math. Soc.
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Precomplete Classes of Automata with the Superposition Operation
Moscow University Mathematics Bulletin, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The superposition operator in ideal spaces
1990In this chapter we are concerned with the basic properties of the superposition operator in so-called ideal spaces which are, roughly speaking, Banach spaces of measurable functions with monotone norm. To formulate our results in a sufficiently general framework, we must introduce a large number of auxiliary notions which will be justified by the ...
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