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Geometric Analysis of PDE and Several Complex Variables: Dedicated to François Treves
Edited by: Sagun Chanillo, Rutgers University, Piscataway, NJ, Paulo D. Cordaro, Instituto de Matemática e Estatística, Universidade de São Paulo, IME-USP, Brazil, Nicholas Hanges, Herbert H. Lehman College, CUNY, Bronx, NY, Jorge Hounie, Universidade Federal de São Carlos, Brazil, and Abdelhamid Meziani, Florida International University, Miami, FL

Contemporary Mathematics
2005; 414 pp; softcover
Volume: 368
ISBN-10: 0-8218-3386-3
ISBN-13: 978-0-8218-3386-5
List Price: US$120
Member Price: US$96
Order Code: CONM/368
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This volume is dedicated to François Treves, who made substantial contributions to the geometric side of the theory of partial differential equations (PDEs) and several complex variables. One of his best-known contributions, reflected in many of the articles here, is the study of hypo-analytic structures.

An international group of well-known mathematicians contributed to the volume. Articles generally reflect the interaction of geometry and analysis that is typical of Treves's work, such as the study of the special types of partial differential equations that arise in conjunction with CR-manifolds, symplectic geometry, or special families of vector fields. There are many topics in analysis and PDEs covered here, unified by their connections to geometry.

The material is suitable for graduate students and research mathematicians interested in geometric analysis of PDEs and several complex variables.


Graduate students and research mathematicians interested in geometric analysis of PDEs and several complex variables.

Table of Contents

  • P. Ahern and X. Gong -- Cusp-type singularities of real analytic curves in the complex plane
  • S. Berhanu and J. Hounie -- The F. and M. Riesz property for vector fields
  • A. Bove -- Gevrey hypo-ellipticity for sums of squares of vector fields: Some examples
  • H. Brezis, P. Mironescu, and A. C. Ponce -- \(W^{1,1}\)-maps with values into \(S^1\)
  • S. Chanillo -- Analytic hypoellipticity and spectral problems for Schrödinger's equation
  • H. Chen and Z. Luo -- Formal solutions for higher order nonlinear totally characteristic PDEs with irregular singularities
  • F. Colombini and N. Lerner -- Uniqueness of \(L^\infty\) solutions for a class of conormal \(BV\) vector fields
  • P. D. Cordaro and N. Hanges -- Impact of lower order terms on a model pde in two variables
  • M. Derridj and D. S. Tartakoff -- Global analytic hypoellipticity for a class of quasilinear sums of squares of vector fields
  • M. Eastwood -- Representations via overdetermined systems
  • G. Francsics and P. D. Lax -- A semi-explicit fundamental domain for a Picard modular group in complex hyperbolic space
  • S. Gindikin -- Complex horospherical transform on real sphere
  • J. Gorsky and A. A. Himonas -- On analyticity in space variable of solutions to the KdV equation
  • L. Hörmander -- The multinomial distribution and some Bergman kernels
  • X. Huang, S. Ji, and D. Xu -- Several results for holomorphic mappings from \(B^n\) into \(B^N\)
  • H. Jacobowitz -- Whitney and Mizohata structures
  • A. E. Kogoj and E. Lanconelli -- One-side Liouville theorems for a class of hypoelliptic ultraparabolic equations
  • L. Lempert -- Acyclic sheaves in Banach spaces
  • A. Li and Y. Y. Li -- A Liouville type theorem for some conformally invariant fully nonlinear equations
  • S. T. Melo -- Norm closure of classical pseudodifferential operators does not contain Hörmander's class
  • G. Métivier -- Remarks on the well-posedness of the nonlinear Cauchy problem
  • A. Meziani -- Representation of solutions of planar elliptic vector fields with degeneracies
  • L. Nirenberg -- Some recollections of working with François Treves
  • M.-C. Shaw -- Boundary value problems on Lipschitz domains in \(\mathbb{R}^n\) or \(\mathbb{C}^n\)
  • S. Spagnolo -- Hyperbolic systems well posed in all Gevrey classes
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