Results 301 to 310 of about 1,266,780 (349)

Nonlinear Superposition Operators

1990
This 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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Nonlinear superposition operators: The superposition operator in Lebesgue spaces

, 1990
J. Appell, P. P. Zabrejko
semanticscholar   +2 more sources

Superposition Operators on Bloch-Type Spaces

Computational Methods and Function Theory, 2007
The 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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Precomplete Classes of Automata with the Superposition Operation

Moscow University Mathematics Bulletin, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Superposition of Substitution Operators

1967
The 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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Uniqueness and numerical method for phaseless inverse diffraction grating problem with known superposition of incident point sources

Inverse Problems
In this paper, we establish the uniqueness of identifying a smooth grating profile with a mixed boundary condition (MBC) or transmission boundary conditions (TBCs) from phaseless data.
Tian Niu, Junliang Lv, Jiahui Gao
semanticscholar   +1 more source

The superposition operator in Orlicz spaces

1990
Whenever 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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The superposition operator in ideal spaces

1990
In 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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On the differentiability of the superposition operator in hölder and Sobolev spaces

Nonlinear Analysis: Theory, Methods & Applications, 1984
A differentiability condition (which is both necessary and sufficient) is given for the superposition operator \(Fu(x)=f(x,u(x))\) between two Hölder spaces. This condition builds on a two-sided estimate for the growth function \(\mu_ F(r)=\sup \{\| Fu\|:\| u\| \leq r\}\) for F on balls of radius r.
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Learning the solution operator of parametric partial differential equations with physics-informed DeepONets

Science Advances, 2021
Sifan Wang, Hanwen Wang
exaly