User:Daviddaved/"Can One Hear the Shape of a Drum?"

Let \lambda_k be the Dirichlet eigenvalues for the domain \Omega, that is, the eigenvalues of the Dirichlet problem for the Laplacian:


\begin{cases}
\Delta u + \lambda u = 0, \\
u|_{\partial \Omega} = 0.
\end{cases}

Since the system above is self-adjoint, the eigenvalues are positive. Two domains are said to be isospectral if they have the same Laplacian eigenvalues.

One can state the discrete analog of the question on graphs...

Last modified on 29 September 2012, at 01:36