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Heisenberg Calculus and Spectral Theory of Hypoelliptic Operators on Heisenberg Manifolds
 
Raphaël S. Ponge University of Toronto, Toronto, ON, Canada
Heisenberg Calculus and Spectral Theory of Hypoelliptic Operators on Heisenberg Manifolds
eBook ISBN:  978-1-4704-0512-0
Product Code:  MEMO/194/906.E
List Price: $73.00
MAA Member Price: $65.70
AMS Member Price: $43.80
Heisenberg Calculus and Spectral Theory of Hypoelliptic Operators on Heisenberg Manifolds
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Heisenberg Calculus and Spectral Theory of Hypoelliptic Operators on Heisenberg Manifolds
Raphaël S. Ponge University of Toronto, Toronto, ON, Canada
eBook ISBN:  978-1-4704-0512-0
Product Code:  MEMO/194/906.E
List Price: $73.00
MAA Member Price: $65.70
AMS Member Price: $43.80
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1942008; 134 pp
    MSC: Primary 58; Secondary 32; 35; 53

    This memoir deals with the hypoelliptic calculus on Heisenberg manifolds, including CR and contact manifolds. In this context the main differential operators at stake include the Hörmander's sum of squares, the Kohn Laplacian, the horizontal sublaplacian, the CR conformal operators of Gover-Graham and the contact Laplacian. These operators cannot be elliptic and the relevant pseudodifferential calculus to study them is provided by the Heisenberg calculus of Beals-Greiner and Taylor.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Heisenberg manifolds and their main differential operators
    • 3. Intrinsic approach to the Heisenberg calculus
    • 4. Holomorphic families of $\Psi _H\mathrm {DOs}$
    • 5. Heat equation and complex powers of hypoelliptic operators
    • 6. Spectral asymptotics for hypoelliptic operators
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
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Volume: 1942008; 134 pp
MSC: Primary 58; Secondary 32; 35; 53

This memoir deals with the hypoelliptic calculus on Heisenberg manifolds, including CR and contact manifolds. In this context the main differential operators at stake include the Hörmander's sum of squares, the Kohn Laplacian, the horizontal sublaplacian, the CR conformal operators of Gover-Graham and the contact Laplacian. These operators cannot be elliptic and the relevant pseudodifferential calculus to study them is provided by the Heisenberg calculus of Beals-Greiner and Taylor.

  • Chapters
  • 1. Introduction
  • 2. Heisenberg manifolds and their main differential operators
  • 3. Intrinsic approach to the Heisenberg calculus
  • 4. Holomorphic families of $\Psi _H\mathrm {DOs}$
  • 5. Heat equation and complex powers of hypoelliptic operators
  • 6. Spectral asymptotics for hypoelliptic operators
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
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