Remote access

How to Order

For AMS eBook frontlist subscriptions or backfile collection purchases:

   1a. To purchase any ebook backfile or to subscibe to the current year of Contemporary Mathematics, please download this required license agreement,

   1b. To subscribe to the current year of Memoirs of the AMS, please download this required license agreement.

   2. Complete and sign the license agreement.

   3. Email, fax, or send via postal mail to:

Customer Services
American Mathematical Society
201 Charles Street Providence, RI 02904-2294  USA
Phone: 1-800-321-4AMS (4267)
Fax: 1-401-455-4046

Visit the AMS Bookstore for individual volume purchases.

Browse the current eBook Collections price list

Powered by MathJax

Wave Front Set of Solutions to Sums of Squares of Vector Fields

About this Title

Paolo Albano, Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40127 Bologna, Italy and Antonio Bove, Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40127 Bologna, Italy

Publication: Memoirs of the American Mathematical Society
Publication Year: 2013; Volume 221, Number 1039
ISBNs: 978-0-8218-7570-4 (print); 978-0-8218-9461-3 (online)
Published electronically: May 21, 2012
Keywords:Analytic Hypoellipticity, FBI Transform, Wave Front Set, Canonical Forms
MSC: Primary 35A18; Secondary 35H10, 35H20

View full volume PDF

View other years and numbers:

Table of Contents


  • Chapter 1. Introduction
  • Chapter 2. The Poisson–Treves stratification
  • Chapter 3. Standard forms for a system of vector fields
  • Chapter 4. Nested strata
  • Chapter 5. Bargman pseudodifferential operators
  • Chapter 6. The “A Priori” estimate on the FBI side
  • Chapter 7. A single symplectic stratum
  • Chapter 8. A single nonsymplectic stratum
  • Chapter 9. Microlocal regularity in nested strata
  • Chapter 10. Known cases and examples
  • Appendix A. A bracket lemma
  • Appendix B. Nonsymplectic strata do not have the reproducing bracket property


We 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. We prove hypoanalyticity for several classes of sums of squares and show that our method, though not general, includes almost every known hypoanalyticity result. Examples are discussed.

References [Enhancements On Off] (What's this?)