Results 281 to 290 of about 51,774 (314)

Planck-Scale Mass Equidistribution of Toral Laplace Eigenfunctions

, 2016
We study the small scale distribution of the L2-mass of eigenfunctions of the Laplacian on the two-dimensional flat torus. Given an orthonormal basis of eigenfunctions, Lester and Rudnick (Commun. Math. Phys. 350(1):279–300, 2017) showed the existence of
A. Granville, I. Wigman
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Generating Spectrum‐Compatible Time Histories Using Eigenfunctions

, 2017
In this article, the causes of drift in the velocity and the displacement time history are investigated. It is found that, in addition to numerical error, drift is caused by overdeterminacy in the constants of integration.
Bo Li, Binh‐Le Ly, W. Xie, M. Pandey
semanticscholar   +1 more source

Orthogonality of Bethe Ansatz Eigenfunctions for the Laplacian on a Hyperoctahedral Weyl Alcove

, 2016
We prove the orthogonality of the Bethe Ansatz eigenfunctions for the Laplacian on a hyperoctahedral Weyl alcove with repulsive homogeneous Robin boundary conditions at the walls.
J. F. van Diejen, E. Emsiz
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On Singularities in Eigenfunctions

The Journal of Chemical Physics, 1965
The relationship between some singularities of the eigenfunction and convergence of the Legendre expansion is studied for the ground state of the helium atom.
openaire   +2 more sources

Small Scale Equidistribution of Eigenfunctions on the Torus

, 2015
We study the small scale distribution of the L2 mass of eigenfunctions of the Laplacian on the flat torus $${\mathbb{T}^{d}}$$Td. Given an orthonormal basis of eigenfunctions, we show the existence of a density one subsequence whose L2 mass ...
S. Lester, Z. Rudnick
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Fall-Off of Eigenfunctions for Non-Local Schrödinger Operators with Decaying Potentials

, 2015
We study the spatial decay of eigenfunctions of non-local Schrödinger operators whose kinetic terms are generators of symmetric jump-paring Lévy processes with Kato-class potentials decaying at infinity.
K. Kaleta, J. Lőrinczi
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On the Number of Nodal Domains of Toral Eigenfunctions

, 2015
We study the number of nodal domains of toral Laplace eigenfunctions. Following Nazarov–Sodin’s results for random fields and Bourgain’s de-randomisation procedure we establish a precise asymptotic result for “generic” eigenfunctions. Our main results in
Jeremiah Buckley, I. Wigman
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Approximation of eigenfunctions in kernel-based spaces

Advances in Computational Mathematics, 2014
Kernel-based methods in Numerical Analysis have the advantage of yielding optimal recovery processes in the “native” Hilbert space ℋ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb ...
G. Santin, R. Schaback
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Nodal sets of Steklov eigenfunctions

, 2014
We study the nodal set of the Steklov eigenfunctions on the boundary of a smooth bounded domain in $$\mathbb {R}^n$$Rn- the eigenfunctions of the Dirichlet-to-Neumann map.
K. Bellová, F. Lin
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Dirichlet eigenfunctions of the square membrane: Courant's property, and A. Stern's and Å. Pleijel's analyses

, 2014
In this paper, we revisit Courant's nodal domain theorem for theDirichlet eigenfunctions of a square membrane, and the analyses ofA. Stern and A. Pleijel.
Pierre B'erard, B. Helffer
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