Results 221 to 230 of about 45,671 (275)

On special orthogonal eigenfunctions and eigenfunction expansions

International Journal of Mathematical Education in Science and Technology, 1996
We extend some earlier results while illustrating solution techniques commonly encountered by students in undergraduate and beginning graduate courses of mathematical analysis, differential equations, and engineering mathematics. Previously, Turan's inequality was established by using a technique known as the Prufer substitution.
openaire   +1 more source

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
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
semanticscholar   +1 more source

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
semanticscholar   +1 more source

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
semanticscholar   +1 more source

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
semanticscholar   +1 more source

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
semanticscholar   +1 more source

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
semanticscholar   +1 more source

Atomic Eigenfunctions and Energies

Physical Review, 1932
In \textsection{}1, the calculation of the nondiagonal elements of electrostatic interaction is sketched. In \textsection{}2, attention is called to the fact that the matrix elements of ${L}_{x}$ (the $x$-component of orbital angular momentum), as calculated between spherical harmonic eigenfunctions taken with positive phase, are negative when ${m}_{l}$
Ufford, C. W., Shortley, G. H.
openaire   +2 more sources