Laguerre Calculus and Its Applications on the Heisenberg Group

Laguerre Calculus and Its Applications on the Heisenberg Group

by Carlos A. Berenstein, Der-Chen E. Chang, Jingzhi Tie
     
 

ISBN-10: 0821827618

ISBN-13: 9780821827611

Pub. Date: 03/01/2001

Publisher: American Mathematical Society

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

Overview

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 Calderon-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.

Product Details

ISBN-13:
9780821827611
Publisher:
American Mathematical Society
Publication date:
03/01/2001
Series:
AMS/IP Studies in Advanced Mathematics Series, #22
Pages:
319
Product dimensions:
7.09(w) x 10.24(h) x (d)

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