Completeness of the Eigenfunctions of the Equilateral Triangle
Copyright policy )Completeness of the Eigenfunctions of the Equilateral Triangle
The Dirichlet problem for the operator -\(\Delta\) in the equilaternal triangle is considered. Explicit expressions for its eigenvalues and eigenfunctions are given in terms of orbits of a certain group G. This group G has six elements and is defined as a set of transformations of \({\mathbb{Z}}^ 2\) generated by operations \(S_ 1: (m,n)\to (m,m-n)\) and \(S_ 2: (m,n)\to (n-m,n)\).
Schrödinger operator, Schrödinger equation, Laplace operator, Transform methods (e.g., integral transforms) applied to PDEs, Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, eigenvalues, orbits, eigenfunctions, Dirichlet problem
Schrödinger operator, Schrödinger equation, Laplace operator, Transform methods (e.g., integral transforms) applied to PDEs, Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, eigenvalues, orbits, eigenfunctions, Dirichlet problem
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).42 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!