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The spectral function μˆ(t)=∑j=1∞exp(−itμj1/2), where {μj}j=1∞ are the eigenvalues of the two-dimensional negative Laplacian, is studiedfor small |t| for a variety of domains, where −∞<t<∞ and i=−1. The dependencies of μˆ(t) on the connectivity of a domain and the Robin boundaryconditions are analyzed. Particular attention is given to anarbitrary multiply-connected drum in ℝ2 together withRobin boundary conditions on its boundaries

The wave equation approach to an inverse eigenvalue problem for an arbitrary multiply connected drum inℝ2with Robin boundary conditions