Spectral Properties of High Contrast Band-Gap Materials and Operators on Graphs

Work of both authors was partially supported by the NSF Grant DMS-9610444 and by a DEPSCoR Grant administered through the ARO. The rst author was also partially supported by an NSF EPSCoR Grant. The content of this article does not necessarily re ect the position or the policy of the federal government. The theory of classical waves in periodic high contrast photonic and acoustic media leads to the spectral problem u = "u,