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The Geometry of Heisenberg Groups

2008 Mathematics
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Release : 2008
Genre : Mathematics
Kind : eBook
Book Rating : 954/5 ( reviews)

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Book Synopsis The Geometry of Heisenberg Groups by : Ernst Binz

Download or read book The Geometry of Heisenberg Groups written by Ernst Binz. This book was released on 2008. Available in PDF, EPUB and Kindle. Book excerpt: "The three-dimensional Heisenberg group, being a quite simple non-commutative Lie group, appears prominently in various applications of mathematics. The goal of this book is to present basic geometric and algebraic properties of the Heisenberg group and its relation to other important mathematical structures (the skew field of quaternions, symplectic structures, and representations) and to describe some of its applications. In particular, the authors address such subjects as signal analysis and processing, geometric optics, and quantization. In each case, the authors present necessary details of the applied topic being considered." "This book manages to encompass a large variety of topics being easily accessible in its fundamentals. It can be useful to students and researchers working in mathematics and in applied mathematics."--BOOK JACKET.

An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem

2007-08-08 Mathematics
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Release : 2007-08-08
Genre : Mathematics
Kind : eBook
Book Rating : 337/5 ( reviews)

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Book Synopsis An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem by : Luca Capogna

Download or read book An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem written by Luca Capogna. This book was released on 2007-08-08. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an up-to-date account of progress on Pansu's celebrated problem on the sub-Riemannian isoperimetric profile of the Heisenberg group. It also serves as an introduction to the general field of sub-Riemannian geometric analysis. It develops the methods and tools of sub-Riemannian differential geometry, nonsmooth analysis, and geometric measure theory suitable for attacks on Pansu's problem.

Geometric Analysis on the Heisenberg Group and Its Generalizations

2008-06-30 Mathematics
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Release : 2008-06-30
Genre : Mathematics
Kind : eBook
Book Rating : 884/5 ( reviews)

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Book Synopsis Geometric Analysis on the Heisenberg Group and Its Generalizations by : Ovidiu Calin

Download or read book Geometric Analysis on the Heisenberg Group and Its Generalizations written by Ovidiu Calin. This book was released on 2008-06-30. Available in PDF, EPUB and Kindle. Book excerpt:

Generalized Heisenberg Groups and Damek-Ricci Harmonic Spaces

2006-11-14 Mathematics
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Release : 2006-11-14
Genre : Mathematics
Kind : eBook
Book Rating : 716/5 ( reviews)

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Book Synopsis Generalized Heisenberg Groups and Damek-Ricci Harmonic Spaces by : Jürgen Berndt

Download or read book Generalized Heisenberg Groups and Damek-Ricci Harmonic Spaces written by Jürgen Berndt. This book was released on 2006-11-14. Available in PDF, EPUB and Kindle. Book excerpt: Generalized Heisenberg groups, or H-type groups, introduced by A. Kaplan, and Damek-Ricci harmonic spaces are particularly nice Lie groups with a vast spectrum of properties and applications. These harmonic spaces are homogeneous Hadamard manifolds containing the H-type groups as horospheres. These notes contain a thorough study of their Riemannian geometry by means of a detailed treatment of their Jacobi vector fields and Jacobi operators. Some problems are included and will hopefully stimulate further research on these spaces. The book is written for students and researchers, assuming only basic knowledge of Riemannian geometry, and it contains a brief survey of the background material needed to follow the entire treatment.

Harmonic Analysis on the Heisenberg Group

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 725/5 ( reviews)

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Book Synopsis Harmonic Analysis on the Heisenberg Group by : Sundaram Thangavelu

Download or read book Harmonic Analysis on the Heisenberg Group written by Sundaram Thangavelu. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: The Heisenberg group plays an important role in several branches of mathematics, such as representation theory, partial differential equations, number theory, several complex variables and quantum mechanics. This monograph deals with various aspects of harmonic analysis on the Heisenberg group, which is the most commutative among the non-commutative Lie groups, and hence gives the greatest opportunity for generalizing the remarkable results of Euclidean harmonic analysis. The aim of this text is to demonstrate how the standard results of abelian harmonic analysis take shape in the non-abelian setup of the Heisenberg group. Thangavelu’s exposition is clear and well developed, and leads to several problems worthy of further consideration. Any reader who is interested in pursuing research on the Heisenberg group will find this unique and self-contained text invaluable.

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