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