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On Generalized Step-Functions and Superposition Operators [PDF]
gmj, 2004 Abstract For a given σ-ideal of sets, the notion of a generalized stepfunction is introduced and investigated in connection with the problem of sup-measurability of certain functions of two variables, regarded as superposition operators.
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Electron vortex beams in nonuniform magnetic fields
Physical Review Research, 2021 We consider the quantum theory of paraxial nonrelativistic electron beams in nonuniform magnetic fields, such as the Glaser field. We find the wave function of an electron from such a beam and show that it is a joint eigenstate of two (z-dependent ...
Abhijeet Melkani, S. J. van Enk
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Journal of High Energy Physics, 2022 The ER = EPR correspondence relates a superposition of entangled, disconnected spacetimes to a connected spacetime with an Einstein-Rosen bridge. We construct examples in which both sides may be described by weakly-coupled string theory.
Daniel Louis Jafferis, Elliot Schneider
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Analytic Morrey Spaces and Bloch-Type Spaces
Journal of Function Spaces, 2018 This paper is devoted to characterizing the boundedness of the Riemann-Stieltjes operators from analytic Morrey spaces to Bloch-type spaces. Moreover, the boundedness of the superposition operator and weighted composition operator on analytic Morrey ...
Ofori Samuel, Jianfei Wang, Yile Zhao
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Continuity properties of the superposition operator [PDF]
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1989 AbstractVarious continuity conditions (in norm, in measure, weakly etc.) for the nonlinear superposition operatorF x(s) =f(s, x(s)) between spaces of measurable functions are established in terms of the generating functionf = f(s, u). In particular, a simple proof is given for the fact that, ifFis continuous in measure, thenfmay be replaced by a ...
Jürgen Appell, Pjotr P. Zabrejko
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Uniform continuity and Brézis–Lieb-type splitting for superposition operators in Sobolev space
Advances in Nonlinear Analysis, 2018 Using concentration-compactness arguments, we prove a variant of the Brézis–Lieb-Lemma under weaker assumptions on the nonlinearity than known before.
Ackermann Nils
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Heralded Optical Entanglement Generation via the Graph Picture of Linear Quantum Networks [PDF]
QuantumNon-destructive heralded entanglement with photons is a valuable resource for quantum information processing. However, they generally entail ancillary particles and modes that amplify the circuit intricacy.
Seungbeom Chin +2 more
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Superpositions for nonlinear operators. I. Strong superpositions and linearizability
Journal of Mathematical Analysis and Applications, 1972 AbstractA notion of superposition for nonlinear operators is defined and strong and weak superpositions are distinguished. The classification and representation of operators having a strong superposition is treated. The algebra induced by the superposition on the domain of operators with strong superpositions, as well as their relation to linearizable ...
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On Measurability Properties Connected with the Superposition Operator
Real Analysis Exchange, 2003 Let \(F\) be a class of real-valued functions defined on some set \(E\), measurable with respect to a \(\sigma\)-algebra \(S\). A function \(\phi: E\times\mathbb{R}\to \mathbb{R}\) is called to be sup-measurable with respect to \(F\) if for each \(f\in F\) the function \(\phi_f\) defined by \(\phi_f(x)= \phi(x,f(x))\) is \(S\)-measurable.
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Computing the magnetic field response of the proton [PDF]
EPJ Web of Conferences, 2020 Background field methods offer an approach through which fundamental non-perturbative hadronic properties can be studied. Lattice QCD is the only ab initio method with which Quantum Chromodynamics can be studied at low energies; it involves numerically ...
Bignell Ryan +2 more
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