The Geometry of Heisenberg Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Geometry of Heisenberg Groups write by Ernst Binz. This book was released on 2008. The Geometry of Heisenberg Groups available in PDF, EPUB and Kindle. "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
An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem write by Luca Capogna. This book was released on 2007-08-08. An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem available in PDF, EPUB and Kindle. 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.
Harmonic Analysis on the Heisenberg Group
Harmonic Analysis on the Heisenberg Group - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Harmonic Analysis on the Heisenberg Group write by Sundaram Thangavelu. This book was released on 2012-12-06. Harmonic Analysis on the Heisenberg Group available in PDF, EPUB and Kindle. 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.
Geometric Analysis on the Heisenberg Group and Its Generalizations
Geometric Analysis on the Heisenberg Group and Its Generalizations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Analysis on the Heisenberg Group and Its Generalizations write by Ovidiu Calin. This book was released on 2008-06-30. Geometric Analysis on the Heisenberg Group and Its Generalizations available in PDF, EPUB and Kindle.
An Introduction to Symplectic Geometry
An Introduction to Symplectic Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Symplectic Geometry write by Rolf Berndt. This book was released on 2001. An Introduction to Symplectic Geometry available in PDF, EPUB and Kindle. Symplectic geometry is a central topic of current research in mathematics. Indeed, symplectic methods are key ingredients in the study of dynamical systems, differential equations, algebraic geometry, topology, mathematical physics and representations of Lie groups. This book is a true introduction to symplectic geometry, assuming only a general background in analysis and familiarity with linear algebra. It starts with the basics of the geometry of symplectic vector spaces. Then, symplectic manifolds are defined and explored. In addition to the essential classic results, such as Darboux's theorem, more recent results and ideas are also included here, such as symplectic capacity and pseudoholomorphic curves. These ideas have revolutionized the subject. The main examples of symplectic manifolds are given, including the cotangent bundle, Kähler manifolds, and coadjoint orbits. Further principal ideas are carefully examined, such as Hamiltonian vector fields, the Poisson bracket, and connections with contact manifolds. Berndt describes some of the close connections between symplectic geometry and mathematical physics in the last two chapters of the book. In particular, the moment map is defined and explored, both mathematically and in its relation to physics. He also introduces symplectic reduction, which is an important tool for reducing the number of variables in a physical system and for constructing new symplectic manifolds from old. The final chapter is on quantization, which uses symplectic methods to take classical mechanics to quantum mechanics. This section includes a discussion of the Heisenberg group and the Weil (or metaplectic) representation of the symplectic group. Several appendices provide background material on vector bundles, on cohomology, and on Lie groups and Lie algebras and their representations. Berndt's presentation of symplectic geometry is a clear and concise introduction to the major methods and applications of the subject, and requires only a minimum of prerequisites. This book would be an excellent text for a graduate course or as a source for anyone who wishes to learn about symplectic geometry.
