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