Layer Potential Techniques in Spectral Analysis

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Introduction
Gohberg-Sigal theory: Generalized argument principle and Rouche's theorem
Eigenvalue perturbation problems and applications: Layer potentials
Eigenvalue perturbations of the Laplacian
Vibration testing for detecting internal corrosion
Perturbations of scattering frequencies of resonators with narrow slits and slots
Eigenvalue perturbations of the Lame system
Photonic and phononic band gaps and optimal design
Floquet transform, spectra of periodic elliptic operators, and quasi-periodic layer potentials
Photonic band gaps Phononic band gaps Optimal design problems
Bibliography
Index
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