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Laguerre Calculus and Its Applications on the Heisenberg Group
 
Carlos Berenstein University of Maryland, College Park, MD
Der-Chen Chang Georgetown University, Washington, DC
Jingzhi Tie University of Georgia, Athens, GA
A co-publication of the AMS and International Press of Boston
Laguerre Calculus and Its Applications on the Heisenberg Group
Hardcover ISBN:  978-0-8218-2761-1
Product Code:  AMSIP/22
List Price: $88.00
MAA Member Price: $79.20
AMS Member Price: $70.40
eBook ISBN:  978-1-4704-3812-8
Product Code:  AMSIP/22.E
List Price: $82.00
MAA Member Price: $73.80
AMS Member Price: $65.60
Hardcover ISBN:  978-0-8218-2761-1
eBook: ISBN:  978-1-4704-3812-8
Product Code:  AMSIP/22.B
List Price: $170.00 $129.00
MAA Member Price: $153.00 $116.10
AMS Member Price: $136.00 $103.20
Laguerre Calculus and Its Applications on the Heisenberg Group
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Laguerre Calculus and Its Applications on the Heisenberg Group
Carlos Berenstein University of Maryland, College Park, MD
Der-Chen Chang Georgetown University, Washington, DC
Jingzhi Tie University of Georgia, Athens, GA
A co-publication of the AMS and International Press of Boston
Hardcover ISBN:  978-0-8218-2761-1
Product Code:  AMSIP/22
List Price: $88.00
MAA Member Price: $79.20
AMS Member Price: $70.40
eBook ISBN:  978-1-4704-3812-8
Product Code:  AMSIP/22.E
List Price: $82.00
MAA Member Price: $73.80
AMS Member Price: $65.60
Hardcover ISBN:  978-0-8218-2761-1
eBook ISBN:  978-1-4704-3812-8
Product Code:  AMSIP/22.B
List Price: $170.00 $129.00
MAA Member Price: $153.00 $116.10
AMS Member Price: $136.00 $103.20
  • Book Details
     
     
    AMS/IP Studies in Advanced Mathematics
    Volume: 222001; 319 pp
    MSC: Primary 22; 33; 42; 43; 47; 32; 30;

    For nearly two centuries, the relation between analytic functions of one complex variable, their boundary values, harmonic functions, and the theory of Fourier series has been one of the central topics of study in mathematics. The topic stands on its own, yet also provides very useful mathematical applications.

    This text provides a self-contained introduction to the corresponding questions in several complex variables: namely, analysis on the Heisenberg group and the study of the solutions of the boundary Cauchy-Riemann equations. In studying this material, readers are exposed to analysis in non-commutative compact and Lie groups, specifically the rotation group and the Heisenberg groups—both fundamental in the theory of group representations and physics.

    Introduced in a concrete setting are the main ideas of the Calderón-Zygmund-Stein school of harmonic analysis. Also considered in the book are some less conventional problems of harmonic and complex analysis, in particular, the Morera and Pompeiu problems for the Heisenberg group, which relates to questions in optics, tomography, and engineering.

    The book was borne of graduate courses and seminars held at the University of Maryland (College Park), the University of Toronto (ON), Georgetown University (Washington, DC), and the University of Georgia (Athens). Readers should have an advanced undergraduate understanding of Fourier analysis and complex analysis in one variable.

    Titles in this series are co-published with International Press of Boston, Inc., Cambridge, MA.

    Readership

    Graduate students and physicists interested in mathematics and the physical sciences; advanced undergraduates and graduate students with knowledge of Fourier analysis and complex analysis in one variable.

  • Table of Contents
     
     
    • Chapters
    • The Laguerre calculus
    • Estimates for powers of the sub-Laplacian
    • Estimates for the spectrum projection operators of the sub-Laplacian
    • The inverse of the operator $\square _{\alpha } = {\sum }^n_{j=1}({X^2_j} - {X^2_{j+n}}) - 2i{\alpha }$T
    • The explicit solution of the $\bar {\partial }$-Neumann problem in a non-isotropic Siegel domain
    • Injectivity of the Pompeiu transform in the isotropic H$_n$
    • Morera-type theorems for holomorphic $\mathcal H^p$ spaces in H$_n$ (I)
    • Morera-type theorems for holomorphic $\mathcal H^p$ spaces in H$_n$ (II)
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 222001; 319 pp
MSC: Primary 22; 33; 42; 43; 47; 32; 30;

For nearly two centuries, the relation between analytic functions of one complex variable, their boundary values, harmonic functions, and the theory of Fourier series has been one of the central topics of study in mathematics. The topic stands on its own, yet also provides very useful mathematical applications.

This text provides a self-contained introduction to the corresponding questions in several complex variables: namely, analysis on the Heisenberg group and the study of the solutions of the boundary Cauchy-Riemann equations. In studying this material, readers are exposed to analysis in non-commutative compact and Lie groups, specifically the rotation group and the Heisenberg groups—both fundamental in the theory of group representations and physics.

Introduced in a concrete setting are the main ideas of the Calderón-Zygmund-Stein school of harmonic analysis. Also considered in the book are some less conventional problems of harmonic and complex analysis, in particular, the Morera and Pompeiu problems for the Heisenberg group, which relates to questions in optics, tomography, and engineering.

The book was borne of graduate courses and seminars held at the University of Maryland (College Park), the University of Toronto (ON), Georgetown University (Washington, DC), and the University of Georgia (Athens). Readers should have an advanced undergraduate understanding of Fourier analysis and complex analysis in one variable.

Titles in this series are co-published with International Press of Boston, Inc., Cambridge, MA.

Readership

Graduate students and physicists interested in mathematics and the physical sciences; advanced undergraduates and graduate students with knowledge of Fourier analysis and complex analysis in one variable.

  • Chapters
  • The Laguerre calculus
  • Estimates for powers of the sub-Laplacian
  • Estimates for the spectrum projection operators of the sub-Laplacian
  • The inverse of the operator $\square _{\alpha } = {\sum }^n_{j=1}({X^2_j} - {X^2_{j+n}}) - 2i{\alpha }$T
  • The explicit solution of the $\bar {\partial }$-Neumann problem in a non-isotropic Siegel domain
  • Injectivity of the Pompeiu transform in the isotropic H$_n$
  • Morera-type theorems for holomorphic $\mathcal H^p$ spaces in H$_n$ (I)
  • Morera-type theorems for holomorphic $\mathcal H^p$ spaces in H$_n$ (II)
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.