Memoirs of the American Mathematical Society 2013; 73 pp; softcover Volume: 221 ISBN10: 0821875701 ISBN13: 9780821875704 List Price: US$62 Individual Members: US$37.20 Institutional Members: US$49.60 Order Code: MEMO/221/1039
 The authors study the (micro)hypoanalyticity and the Gevrey hypoellipticity of sums of squares of vector fields in terms of the PoissonTreves stratification. The FBI transform is used. They prove hypoanalyticity for several classes of sums of squares and show that their method, though not general, includes almost every known hypoanalyticity result. Examples are discussed. Table of Contents  Introduction
 The PoissonTreves stratification
 Standard forms for a system of vector fields
 Nested strata
 Bargman pseudodifferential operators
 The "a priori" estimate on the FBI side
 A single symplectic stratum
 A single nonsymplectic stratum
 Microlocal regularity in nested strata
 Known cases and examples
 Appendix A. A bracket lemma
 Appendix B. Nonsymplectic strata do not have the reproducing bracket property
 Bibliography
 Index
