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
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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