Contemporary Mathematics 2005; 414 pp; softcover Volume: 368 ISBN10: 0821833863 ISBN13: 9780821833865 List Price: US$120 Member Price: US$96 Order Code: CONM/368
 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 bestknown contributions, reflected in many of the articles here, is the study of hypoanalytic structures. An international group of wellknown 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 CRmanifolds, 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. Readership Graduate students and research mathematicians interested in geometric analysis of PDEs and several complex variables. Table of Contents  P. Ahern and X. Gong  Cusptype 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 hypoellipticity 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 semiexplicit 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  Oneside 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 wellposedness 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
