Geometric Analysis of PDE and Several Complex Variables : Dedicated to François Treves.

Intro -- Contents -- Cusp-type singularities of real analytic curves in the complex plane -- The F. and M. Riesz property for vector fields -- Gevrey hypo-ellipticity for sums of squares of vector fields: Some examples -- 1. Introduction -- 2. Statement of the Treves conjecture -- 3. The case of a nonsymplectic Poisson stratification: some definitions -- 4. Proof of Theorem 1.0.1 -- 5. The Poisson-Treves stratification for Ls and Li -- 6. Symplectic slices and Gevrey Hypo-Ellipticity -- References -- W1,1-maps with values into S1 -- Analytic hypoellipticity and spectral problems for Schrödinger's equation -- Formal solutions for higher order nonlinear totally characteristic PDEs with irregular singularities -- Uniqueness of L∞ solutions for a class of conormal BV vector fields -- Impact of lower order terms on a model PDE in two variables -- Global analytic hypoellipticity for a class of quasilinear sums of squares of vector fields -- Representations via overdetermined systems -- A semi-explicit fundamental domain for a Picard modular group in complex hyperbolic space -- Complex horospherical transform on real sphere -- On analyticity in space variable of solutions to the KdV equation -- The multinomial distribution and some Bergman kernels -- Several results for holomorphic mappings from Bn into BN -- Whitney and Mizohata structures -- One-side Liouville theorems for a class of hypoelliptic ultraparabolic equations -- Acyclic sheaves in Banach spaces -- A Liouville type theorem for some conformally invariant fully nonlinear equations -- Norm closure of classical pseudodifferential operators does not contain Hörmander's class -- Remarks on the well-posedness of the nonlinear Cauchy problem -- Representation of solutions of planar elliptic vector fields with degeneracies -- Some recollections of working with François Treves.

Boundary values problems on Lipschitz domains in Rn or Cn -- Hyperbolic systems well posed in all Gevrey classes.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.