Noncommutative Microlocal Analysis
Author: Michael Eugene Taylor
Publisher: American Mathematical Soc.
Published: 1984
Total Pages: 188
ISBN-13: 0821823140
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Engineering Applications of Noncommutative Harmonic Analysis
Author: Gregory S. Chirikjian
Publisher: CRC Press
Published: 2000-09-28
Total Pages: 698
ISBN-13: 1420041762
DOWNLOAD EBOOKThe classical Fourier transform is one of the most widely used mathematical tools in engineering. However, few engineers know that extensions of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. For those that may be aware of its potential value, there is sti
Non-Abelian Harmonic Analysis
Author: Roger E. Howe
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 271
ISBN-13: 1461392004
DOWNLOAD EBOOKThis book mainly discusses the representation theory of the special linear group 8L(2, 1R), and some applications of this theory. In fact the emphasis is on the applications; the working title of the book while it was being writ ten was "Some Things You Can Do with 8L(2). " Some of the applications are outside representation theory, and some are to representation theory it self. The topics outside representation theory are mostly ones of substantial classical importance (Fourier analysis, Laplace equation, Huyghens' prin ciple, Ergodic theory), while the ones inside representation theory mostly concern themes that have been central to Harish-Chandra's development of harmonic analysis on semisimple groups (his restriction theorem, regularity theorem, character formulas, and asymptotic decay of matrix coefficients and temperedness). We hope this mix of topics appeals to nonspecialists in representation theory by illustrating (without an interminable prolegom ena) how representation theory can offer new perspectives on familiar topics and by offering some insight into some important themes in representation theory itself. Especially, we hope this book popularizes Harish-Chandra's restriction formula, which, besides being basic to his work, is simply a beautiful example of Fourier analysis on Euclidean space. We also hope representation theorists will enjoy seeing examples of how their subject can be used and will be stimulated by some of the viewpoints offered on representation-theoretic issues.
Non-Commutative Harmonic Analysis
Author: Jacques Carmona
Publisher:
Published: 1979
Total Pages: 244
ISBN-13:
DOWNLOAD EBOOKRepresentation Theory and Noncommutative Harmonic Analysis II
Author: A.A. Kirillov
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 274
ISBN-13: 3662097567
DOWNLOAD EBOOKTwo surveys introducing readers to the subjects of harmonic analysis on semi-simple spaces and group theoretical methods, and preparing them for the study of more specialised literature. This book will be very useful to students and researchers in mathematics, theoretical physics and those chemists dealing with quantum systems.
Non-commutative Analysis
Author: Palle Jorgensen
Publisher: World Scientific
Published: 2017-01-24
Total Pages: 562
ISBN-13: 9813202149
DOWNLOAD EBOOK'This is a book to be read and worked with. For a beginning graduate student, this can be a valuable experience which at some points in fact leads up to recent research. For such a reader there is also historical information included and many comments aiming at an overview. It is inspiring and original how old material is combined and mixed with new material. There is always something unexpected included in each chapter, which one is thankful to see explained in this context and not only in research papers which are more difficult to access.'Mathematical Reviews ClippingsThe book features new directions in analysis, with an emphasis on Hilbert space, mathematical physics, and stochastic processes. We interpret 'non-commutative analysis' broadly to include representations of non-Abelian groups, and non-Abelian algebras; emphasis on Lie groups and operator algebras (C* algebras and von Neumann algebras.)A second theme is commutative and non-commutative harmonic analysis, spectral theory, operator theory and their applications. The list of topics includes shift invariant spaces, group action in differential geometry, and frame theory (over-complete bases) and their applications to engineering (signal processing and multiplexing), projective multi-resolutions, and free probability algebras.The book serves as an accessible introduction, offering a timeless presentation, attractive and accessible to students, both in mathematics and in neighboring fields.
Noncommutative Harmonic Analysis
Author: Michael Eugene Taylor
Publisher: American Mathematical Soc.
Published: 1986
Total Pages: 346
ISBN-13: 0821815237
DOWNLOAD EBOOKExplores some basic roles of Lie groups in linear analysis, with particular emphasis on the generalizations of the Fourier transform and the study of partial differential equations.
A First Course in Harmonic Analysis
Author: Anton Deitmar
Publisher: Springer Science & Business Media
Published: 2013-04-17
Total Pages: 154
ISBN-13: 147573834X
DOWNLOAD EBOOKThis book introduces harmonic analysis at an undergraduate level. In doing so it covers Fourier analysis and paves the way for Poisson Summation Formula. Another central feature is that is makes the reader aware of the fact that both principal incarnations of Fourier theory, the Fourier series and the Fourier transform, are special cases of a more general theory arising in the context of locally compact abelian groups. The final goal of this book is to introduce the reader to the techniques used in harmonic analysis of noncommutative groups. These techniques are explained in the context of matrix groups as a principal example.
Principles of Harmonic Analysis
Author: Anton Deitmar
Publisher: Springer
Published: 2014-06-21
Total Pages: 330
ISBN-13: 3319057928
DOWNLOAD EBOOKThis book offers a complete and streamlined treatment of the central principles of abelian harmonic analysis: Pontryagin duality, the Plancherel theorem and the Poisson summation formula, as well as their respective generalizations to non-abelian groups, including the Selberg trace formula. The principles are then applied to spectral analysis of Heisenberg manifolds and Riemann surfaces. This new edition contains a new chapter on p-adic and adelic groups, as well as a complementary section on direct and projective limits. Many of the supporting proofs have been revised and refined. The book is an excellent resource for graduate students who wish to learn and understand harmonic analysis and for researchers seeking to apply it.
Harmonic Analysis on the Heisenberg Group
Author: Sundaram Thangavelu
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 204
ISBN-13: 1461217725
DOWNLOAD EBOOKThe 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.
