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Phase Space Analysis of Partial Differential Equations

Pseudodifferential and paradifferential calculus

speaker: Jean-Michel Bony (Ecole Polytechnique)

abstract: - Littlewood-Paley theory, characterization of Sobolev and Hölder spaces - Decomposition of classical symbols; boundedness in $L2$ - Oscillatory integrals - Classical pseudodifferential operators, symbolic calculus, wave front - Classes $S^m_{\rho,0}$ and hypoelliptic operators of constant strength - Brief survey of the $S_{\rho,\delta }$ calculus and of the Weyl-Hörmander calculus - Paraproduct, paradifferential operators, symbolic calculus - Paralinearization of nonlinear differential equations - Microlocal ellipticity - Propagation of singularities.

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