#### How to Order

For AMS eBook frontlist subscriptions or backfile collection purchases:

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
Email: cust-serv@ams.org

Visit the AMS Bookstore for individual volume purchases.

# memo_has_moved_text(); Wave Front Set of Solutions to Sums of Squares of Vector Fields

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)
DOI: http://dx.doi.org/10.1090/S0065-9266-2012-00663-0
Posted: May 21, 2012
Keywords: Analytic Hypoellipticity, FBI Transform, Wave Front Set, Canonical Forms
MSC (2010): Primary 35A18; Secondary 35H10, 35H20

View full volume PDF

View other years and numbers:

Chapters

• 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

### Abstract

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.