Results 11 to 20 of about 45,671 (275)
Lower bounds for Steklov eigenfunctions [PDF]
Pure and Applied Mathematics Quarterly, 2021 Let $(\Omega,g)$ be a compact, analytic Riemannian manifold with analytic boundary $\partial \Omega = M.$ We give $L^2$-lower bounds for Steklov eigenfunctions and their restrictions to interior hypersurfaces $H \subset \Omega^{\circ}$ in a geometrically
J. Galkowski, J. Toth
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On local and global structures of transmission eigenfunctions and beyond [PDF]
Journal of Inverse and Ill-Posed Problems, 2020 The (interior) transmission eigenvalue problems are a type of non-elliptic, non-selfadjoint and nonlinear spectral problems that arise in the theory of wave scattering.
Hongyu Liu
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Data-driven discovery of Koopman eigenfunctions for control [PDF]
Machine Learning: Science and Technology, 2017 Data-driven transformations that reformulate nonlinear systems in a linear framework have the potential to enable the prediction, estimation, and control of strongly nonlinear dynamics using linear systems theory.
E. Kaiser, J. Kutz, S. Brunton
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Optimal Construction of Koopman Eigenfunctions for Prediction and Control [PDF]
IEEE Transactions on Automatic Control, 2018 This article presents a novel data-driven framework for constructing eigenfunctions of the Koopman operator geared toward prediction and control. The method leverages the richness of the spectrum of the Koopman operator away from attractors to construct ...
Milan Korda, I. Mezić
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Extended Dynamic Mode Decomposition with Learned Koopman Eigenfunctions for Prediction and Control [PDF]
American Control Conference, 2019 This paper presents a novel learning framework to construct Koopman eigenfunctions for unknown, nonlinear dynamics using data gathered from experiments. The learning framework can extract spectral information from the full non-linear dynamics by learning
C. Folkestad +5 more
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Control of eigenfunctions on surfaces of variable curvature [PDF]
Journal of The American Mathematical Society, 2019 We prove a microlocal lower bound on the mass of high energy eigenfunctions of the Laplacian on compact surfaces of negative curvature, and more generally on surfaces with Anosov geodesic flows.
S. Dyatlov, Long Jin, S. Nonnenmacher
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Nonradiating Sources and Transmission Eigenfunctions Vanish at Corners and Edges [PDF]
SIAM Journal on Mathematical Analysis, 2018 We consider the inverse source problem of a fixed wavenumber: study properties of an acoustic source based on a single far- or near-field measurement. We show that nonradiating sources having a convex or non-convex corner or edge on their boundary must ...
Eemeli Blåsten
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Localization of eigenfunctions via an effective potential [PDF]
Communications in Partial Differential Equations, 2017 We consider the localization of eigenfunctions for the operator on a Lipschitz domain Ω and, more generally, on manifolds with and without boundary. In earlier work, two authors of the present paper demonstrated the remarkable ability of the landscape ...
D. Arnold +4 more
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Comparison of Direct and Adjoint k and α-Eigenfunctions
Journal of Nuclear Engineering, 2021 Modal expansions based on k-eigenvalues and α-eigenvalues are commonly used in order to investigate the reactor behaviour, each with a distinct point of view: the former is related to fission generations, whereas the latter is related to time. Well-known
Vito Vitali +4 more
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Scattering by Curvatures, Radiationless Sources, Transmission Eigenfunctions, and Inverse Scattering Problems [PDF]
SIAM Journal on Mathematical Analysis, 2018 We consider several intriguingly connected topics in the theory of wave propagation: geometrical characterizations of radiationless sources, non-radiating incident waves and interior transmission eigenfunctions, and their applications to inverse ...
Eemeli Blåsten, Hongyu Liu
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