Index
adjoint, 26
almost orthogonality, 78
asymptotic sum, 22
bicharacteristic (curve), 116
Cauchy problem, 93
change of variables, 37
characteristic (surface), 111
commutator, 40
continuity, L
2
, 30
convexity inequalities, 82
cotangent bundle, 29
density on a manifold, 74
Dirichlet problem, 124
elliptic (symbol, operator), 33
energy (inequality), 98
1-form, canonical, 39
2-form, symplectic, 39
factorization (of an operator), 103
Fourier distribution, 91
Fourier transform, 11
Garding inequality, 31
Gagliardo-Nirenberg inequality, 86
Hamiltonian (vector field), 40
Holder spaces, 80
Hormander's theorem, 102
hyperbolic (operator, system), 103
implicit function theorem, 121, 122
interpolation, 108
isometric embedding, 133
kernels, 9
Laplacian, 16
Littlewood-Paley decomposition, 77
local inversion theorem, 121
local symbol, 35
Meyer multiplier, 87
Morse's lemma, 69
Newton schenie, 146
non-stationary phase, 41
operator on a manifold, 37
oscillatory integral, 41
parametrix, 17
paraproduct, 86
partition of unity, 7, 36
Poisson bracket, 29
principal symbol, 27
propagation of singularities, 101
properly supported operator, 36
pseudo-differential operator, 15, 24
pseudo-local property, 19
quasilinear system, 128
Rauch's lemma, 113
regularization operator, 83
singular integral, 60
small divisors, 138
Sobolev space, 31
