**Contemporary Mathematics**

Volume: 205;
1997;
276 pp;
Softcover

MSC: Primary 32; 35;

Print ISBN: 978-0-8218-0509-1

Product Code: CONM/205

List Price: $71.00

Individual Member Price: $56.80

**Electronic ISBN: 978-0-8218-7796-8
Product Code: CONM/205.E**

List Price: $71.00

Individual Member Price: $56.80

# Multidimensional Complex Analysis and Partial Differential Equations

Share this page *Edited by *
*Paulo D. Cordaro; Howard Jacobowitz*

This collection of papers by outstanding contributors in analysis, partial differential equations, and several complex variables is dedicated to Professor François Treves in honor of his 65th birthday. There are five important survey articles covering analytic singularities, holomorphically nondegenerate algebraic hypersurfaces, analyticity of CR mappings, removable singularities of vector fields, and local solvability for systems of vector fields. The other papers are original research contributions on topics such as Klein-Gordon and Dirac equations, Toeplitz operators, elliptic structures, complexification of Lie groups, pseudo-differential operators, nonlinear equations, CR and Mizohata structures, analytic hypoellipticity, overdetermined systems, and group invariant convex hypersurfaces.

#### Table of Contents

# Table of Contents

## Multidimensional Complex Analysis and Partial Differential Equations

- Contents vii8 free
- Preface ix10 free
- On extreme points and the strong maximum principle for CR functions 112 free
- Symplectic cones and Toeplitz operators 1526
- A Lyapounov-Schmidt procedure involving a nonlinear projection 2536
- Remarks on commutators of pseudo-differential operators 3344
- A survey on the problem of local solvability for systems of vector fields 3950
- Extension of CR-structures for 3-dimensional pseudoconcave manifolds 5162
- Analytic singularities 6980
- Asymptotic behavior of the Bergman kernel and hypergeometric functions 7990
- Quasilinear degenerate elliptic equations in divergence form 93104
- Remarks on the Klein-Gordon and Dirac equations 101112
- Removable singularities of vector fields and the Nirenberg-Treves property 127138
- The Levi and Stein problems for elliptic structures 141152
- On a priori estimate on a manifold with singularity on the boundary 155166
- The problem of complexifying a Lie group 169180
- Energy methods via coherent states and advanced pseudo-differential calculus 177188
- Group invariant convex hypersurfaces with prescribed Gauss-Kronecker curvature 203214
- Elliptic structures 219230
- Mizohata structures on S2: Automorphisms and standardness 235246
- Holomorphically nondegenerate algebraic hypersurfaces and their mappings 247258
- Analyticity of CR mappings of algebraic hypersurfaces 253264
- Propagation of extendibility of CR functions on manifolds with edges 259270
- A note on extremal discs and double valued reflection 271282

#### Readership

Graduate students and research mathematicians interested in analysis, differential equations and several complex variables.