Here, using these methods for the Helmholtz and modified Helmholtz equations and following the earlier results of [15] , we determine eigenvalues of the Laplacian in a convex polygon. Eigenvalues are characterised by the points where the generalised Dirichlet to Neumann map becomes singular. We ...
Expansions are extracted by considering the restorative force term as a linear perturbation of the Laplacian; errors of truncation for these expansions are estimated. Theriteria defining the subset of eigenvalues and eigenfunctions that can be studied depends only on the size and linearity of the ...
This work also presents the highly accurate computation of eigenfunctions and eigenvalues with cubic finite elements on triangle meshes and discusses the construction of persistence diagrams from the Morse-Smale complex as well as the relation to size functions....
Toth and Steve Zelditch Abstract. The eigenfunctions ei λ,x of the Laplacian on a flat torus have uniformly bounded Lp norms. In this article, we prove that for every other quantum inte- grable Laplacian, the Lp norms of the joint eigenfunctions blow up at least at the rate ϕk Lp ...
Let $(M,g)$ be a two-dimensional compact boundaryless Riemannian manifoldwith Laplacian, $\\Delta_g$. If $e_\\lambda$ are the associated eigenfunctions of$\\sqrt{-\\Delta_g}$ so that $-\\Delta_g e_\\lambda = \\lambda^2 e_\\lambda$, then ithas been known for some time \\...
eigenvaluesand eigenfunctionsof theFPoperator providenew insightsinto theproperties of theseeigenvectorsandontheperformanceof spectral clusteringalgorithms, asdescribed in section 4. 2 Diffusion Distances and Diffusion Maps Thestarting point of our analysis, as also noted in other works, is theobservation th...
摘要: This expository note explores Laplacian eigenfunction localization for compact domains. We work in the context of a particular numerically determined, localized, low frequency eigenfunction.关键词:中国 信息技术 软件产业 国际化 DOI: 10.5565/PUBLMAT_50106_13 被引量: 23 ...
Eigenvalues and eigenfunctions of one-dimensional fractal Laplacians defined by iterated function systems with overlaps[J].Journal of Mathematical Analysis and Applications 2010,1(1).J. Chen, S.M. Ngai, Eigenvalues and eigenfunctions of one-dimensional fractal Laplacians defined by iterated function ...
Eigenvalues and Eigenfunctions of the LaplacianNica, MihaiNica, M., 2011: Eigenvalues and Eigenfunctions of the Laplacian, The Waterloo Mathematics Review, 1, 23-34.M. Nica. Eigenvalues and Eigenfunctions of the Laplacian. The Waterloo Mathe- matics Review, 1(2):23-34, 2011....
M. M. H. Pang: Approximation of ground state eigenvalues and eigenfunctions of Dirichlet Laplacians. Bull. London Math. Soc. 29 (1997) 720–730.M.M.H. Pang, Approximation of ground state eigenvalues of eigenfunctions of Dirichlet Laplacians. Bull. London Math. Soc. 29(1997), 720-730....