Spectrum of Laplician on Triangles(IV)
Qiu Wei-gang · 2009
The eigenfunctions of some triangles with symmetric group,such as right angle isosceles,transform as one dimensional representation of this point group.In this paper,the eigenfunctions are constructed from the four one dimensional representation of dihedral group(n=4),which corresponding to four boundaries conditions(BC).The eigenvectors are set by the four BC.The zeta functions and heat kernels are also derived.The completeness of eigenfunctions is confirmed by the first two heat kernel coefficients.Some legacy problems are also discussed.