Phase Space Analysis of Partial Differential

This collection of original articles and surveys treats the linear and nonlinear aspects of the theory of partial differential equations. Phase space analysis methods, including microlocal analysis, have yielded striking results in past years and have become one of the main tools of investigation. Equally important is their role in many applications to physics, for example, in quantum and spectral theories.Key topics:* The Cauchy problem for linear and nonlinear hyperbolic equations* Scattering theory* Inverse problems* Hyperbolic systems* Gevrey regularity of solutions of PDEs* Analytic hypoellipticityand unique features:* Original articles are self-contained with full proofs* Survey articles give a quick and direct introduction to selected topics evolving at a fast paceGraduate students at various levels as well as researchers in PDEs and related fields will find this an excellent resource.

Preface	p. vii
List of Contributors	p. xi
Trace theorem on the Heisenberg group on homogeneous hypersurfaces	p. 1
Strong unique continuation and finite jet determination for Cauchy-Riemann mappings	p. 17
On the Cauchy problem for some hyperbolic operator with double characteristics	p. 29
On the differentiability class of the admissible square roots of regular nonnegative functions	p. 45
The Benjamin-Ono equation in energy space	p. 55
Instabilities in Zakharov equations for laser propagation in a plasma	p. 63
Symplectic strata and analytic hypoellipticity	p. 83
On the backward uniqueness property for a class of parabolic operators	p. 95
Inverse problems for hyperbolic equations	p. 107
On the optimality of some observability inequalities for plate systems with potentials	p. 117
Some geometric evolution equations arising as geodesic equations on groups of diffeomorphisms including the Hamiltonian approach	p. 133
Non-effectively hyperbolic operators and bicharacteristics	p. 217
On the Fefferman-Phong inequality for systems of PDEs	p. 247
Local energy decay and Strichartz estimates for the wave equation with time-periodic perturbations	p. 267
An elementary proof of Fedii's theorem and extensions	p. 287
Outgoing parametrices and global Strichartz estimates for Schrodinger equations with variable coefficients	p. 291
On the analyticity of solutions of sums of squares of vector fields	p. 315
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Phase Space Analysis of Partial Differential Equations

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