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Wave Front Set of Solutions to Sums of Squares of Vector Fields
 
Paolo Albano Università di Bologna, Bologna, Italy
Antonio Bove Università di Bologna, Bologna, Italy
Wave Front Set of Solutions to Sums of Squares of Vector Fields
eBook ISBN:  978-0-8218-9461-3
Product Code:  MEMO/221/1039.E
List Price: $62.00
MAA Member Price: $55.80
AMS Member Price: $37.20
Wave Front Set of Solutions to Sums of Squares of Vector Fields
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Wave Front Set of Solutions to Sums of Squares of Vector Fields
Paolo Albano Università di Bologna, Bologna, Italy
Antonio Bove Università di Bologna, Bologna, Italy
eBook ISBN:  978-0-8218-9461-3
Product Code:  MEMO/221/1039.E
List Price: $62.00
MAA Member Price: $55.80
AMS Member Price: $37.20
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2212013; 73 pp
    MSC: Primary 35;

    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
     
     
    • Chapters
    • 1. Introduction
    • 2. The Poisson–Treves Stratification
    • 3. Standard Forms for a System of Vector Fields
    • 4. Nested Strata
    • 5. Bargman Pseudodifferential Operators
    • 6. The “A Priori” Estimate on the FBI Side
    • 7. A Single Symplectic Stratum
    • 8. A Single Nonsymplectic Stratum
    • 9. Microlocal Regularity in Nested Strata
    • 10. Known Cases and Examples
    • A. A Bracket Lemma
    • B. Nonsymplectic Strata Do Not Have the Reproducing Bracket Property
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2212013; 73 pp
MSC: Primary 35;

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.

  • Chapters
  • 1. Introduction
  • 2. The Poisson–Treves Stratification
  • 3. Standard Forms for a System of Vector Fields
  • 4. Nested Strata
  • 5. Bargman Pseudodifferential Operators
  • 6. The “A Priori” Estimate on the FBI Side
  • 7. A Single Symplectic Stratum
  • 8. A Single Nonsymplectic Stratum
  • 9. Microlocal Regularity in Nested Strata
  • 10. Known Cases and Examples
  • A. A Bracket Lemma
  • B. Nonsymplectic Strata Do Not Have the Reproducing Bracket Property
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.