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

< User:Daviddaved

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

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...