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

< User:Daviddaved

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

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

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...