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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 2012: 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
Published electronically: May 21, 2012
Keywords: Analytic Hypoellipticity, FBI Transform, Wave Front Set, Canonical Forms
MSC (2010): Primary 35A18; Secondary 35H10, 35H20

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Table of Contents


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.

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