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Wave Front Set of Solutions to Sums of Squares of Vector Fields
Paolo Albano and Antonio Bove, Università di Bologna, Italy

Memoirs of the American Mathematical Society
2013; 73 pp; softcover
Volume: 221
ISBN-10: 0-8218-7570-1
ISBN-13: 978-0-8218-7570-4
List Price: US$62
Individual Members: US$37.20
Institutional Members: US$49.60
Order Code: MEMO/221/1039
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The authors study the (micro)hypoanalyticity and the Gevrey hypoellipticity of sums of squares of vector fields in terms of the Poisson-Treves 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 Poisson-Treves 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
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