Index arclength parametrization, 54 argument principle, 7, 91 asymptotic expansion, 35, 39, 40, 43, 58, 98, 138, 139, 142 band function, 122 Bessel function, 129 Bethe-Sommerfeld conjecture, 123 boundary integral method, 64, 133 Brillouin zone, 121, 123, 126, 134, 137, 154, 186 capacity, 22, 41, 103, 108 characteristic value, 9, 136, 138, 149 compact operator, 8, 31 conormal derivative, 29, 127 corrosion, 77 density result, 80 direct fiber decomposition, 122 direct integral, 122 Dirichlet-to-Neumann map, 21, 133, 145, 167 dispersion relation, 122 double-layer potential, 20, 23, 29 duality, 20 effective medium theory, 50, 109 eigenvalue, 25, 33, 78, 124 eigenvalue perturbation, 35, 77, 98, 103 eigenvalue problem, 91 eigenvector, 9 elastic moment tensor, 109 Ewald’s method, 128 factorization, 8, 11, 13 fiber waveguide, 134 finite Hilbert transform, 93, 94 finitely meromorphic operator, 10, 11 Floquet condition, 121 Floquet theory, 154, 155 Floquet transform, 121 Fourier transform, 121, 126 Fr´ echet derivative, 181, 182 Fredholm alternative, 8, 11, 160 Fredholm operator, 8, 11, 97, 134, 136, 154 fundamental solution, 20, 22, 28, 29 Gˆ ateaux derivative, 187 generalized argument principle, 12, 14, 39, 61 generalized gradient, 187 generalized Rouch´ e’s theorem, 12, 14, 86, 91, 97, 98, 103, 133, 134, 137, 139, 154, 159, 162 geometric multiplicity, 60 Giorgi-Nash method, 69 gradient flow, 180 Graf’s addition theorem, 129 Green’s formula, 23, 30 grounded inclusion, 35 Hamilton-Jacobi equation, 180, 182 Hankel function, 22, 123, 129 hard inclusion, 103, 104 Hashin-Shtrikman bounds, 50, 63, 110, 116 Hausdorff measure, 77, 78, 81 heat kernel, 130 Helmholtz equation, 22, 30, 78, 123 Helmholtz resonator, 99, 151 high contrast, 133, 154 Hilbert inversion formula, 94, 95, 99 ill-posedness, 77 index, 9 inverse Fourier transform, 126 jump formula, 21, 23, 29, 124, 127 Kelvin matrix, 29 Kummer’s transformation, 128, 130 Kupradze matrix, 28 Lagrange multiplier, 180 Lam´ e system, 28, 103, 126, 154 Laplace equation, 20 Laplace transform, 130 lattice sum representation, 128, 129 Laurent series expansion, 10 layer potentials, 19, 123, 124 201

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