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

摘要

The spectral functionμˆ(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<∞andi=−1. The dependencies ofμˆ(t)on the connectivity of a domain and the Robin boundaryconditions are analyzed. Particular attention is given to anarbitrary multiply-connected drum inℝ2together withRobin boundary conditions on its boundaries.