The Analysis of Linear Partial Differential Operators |
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analytic assume asymptotic bundle C₁ C₂ canonical relation canonical transformation Cauchy choose coefficients commutator completes the proof conic neighborhood constant coordinates D₁ defined definition derivatives differential operators dimensional bicharacteristic eigenvalues elliptic operators equal estimate factor fixed follows from Theorem Fourier integral operators Fourier transform G₁ gives Hamilton field Hence homogeneous function homogeneous of degree Hörmander hypothesis implies kernel Lagrangian Lemma linear manifold Math microlocally multiplication N₂ non-characteristic norm notation obtain p₁ partial differential equations phase function Poisson brackets polynomial positive principal symbol proof of Proposition proof of Theorem properly supported prove pseudo-differential operator Pure Appl replaced right-hand side Section self-adjoint small conic neighborhood solution solvability subelliptic sufficiently supp symplectic tangent term uniformly bounded V¹(x values vanishes variables vector field wave front set x₁