Author
Selden, Jeffrey LeeIssue Date
2004Keywords
Mathematics.Advisor
Friedlander, Leonid
Metadata
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The University of Arizona.Rights
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.Abstract
This dissertation studies the asymptotic behavior for the integrated density of states function for operators associated with the propagation of classical waves in a high-contrast, periodic, two-component medium. Consider a domain Ω₊ contained in the hypercube [0, 2π)ⁿ. We define a function χ(τ) which takes the value 1 in Ω₊ and the value τ in [0, 2π)\Ω₊. We extend this setup periodically to Rⁿ and define the operator L(τ) = -∇χ(τ)∇. As τ → ∞, it is known that the spectrum of L(τ) exhibits a band-gap structure and that the spectral density accumulates at the upper endpoints of the bands. We establish the existence and some important properties of a rescaled integrated density of states function in the large coupling limit which describes the non-trivial asymptotic behavior of this spectral accumulation.Type
textDissertation-Reproduction (electronic)
Degree Name
Ph.D.Degree Level
doctoralDegree Program
Graduate CollegeMathematics