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| Author | : Michael Eugene Taylor |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 188 |
| Release | : 1984 |
| Genre | : Differential equations, Hypoelliptic |
| ISBN | : 0821823140 |
| Author | : Gregory S. Chirikjian |
| Publisher | : CRC Press |
| Total Pages | : 698 |
| Release | : 2000-09-28 |
| Genre | : Computers |
| ISBN | : 1420041762 |
The 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
| Author | : A.A. Kirillov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 274 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 3662097567 |
Two 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.
| Author | : Jacques Carmona |
| Publisher | : |
| Total Pages | : 244 |
| Release | : 1979 |
| Genre | : |
| ISBN | : |
| Author | : Anton Deitmar |
| Publisher | : Springer |
| Total Pages | : 330 |
| Release | : 2014-06-21 |
| Genre | : Mathematics |
| ISBN | : 3319057928 |
This 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.
| Author | : Anton Deitmar |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 154 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 147573834X |
This 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.
| Author | : Jorgensen Palle |
| Publisher | : World Scientific |
| Total Pages | : 564 |
| Release | : 2017-01-24 |
| Genre | : Mathematics |
| ISBN | : 9813202149 |
The 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.
| Author | : Michael Eugene Taylor |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 346 |
| Release | : 1986 |
| Genre | : Mathematics |
| ISBN | : 0821815237 |
Explores 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.
| Author | : Raymond C. Fabec |
| Publisher | : |
| Total Pages | : 529 |
| Release | : 2014-07-06 |
| Genre | : Fourier analysis |
| ISBN | : 9780991326600 |
This is a graduate text on harmonic analysis. It begins with a chapter on Fourier series. The next two chapters are spent covering function theory on real spaces and the classical Fourier transform. Following this is a chapter covering the Paley-Wiener Theorem, distributions, convolution, the Sobolev Lemma, the Shannon Sampling Theorem, windowed and wavelet transforms, and the Poisson summation formula. The later chapters deal with non-commutative theory. Topics include abstract homogeneous spaces and fundamentals of representation theory. These are used in the last two chapters. The first covers the Heisenberg group which encode the Heisenberg uncertainty principle. This is first instance of the use of infinite dimensional representations. The last covers the basic theory of compact groups. Here finite dimensionality is sufficient. Spherical functions and Gelfand pairs are discussed. There is also a section on finite groups. The text is interspersed with over 50 exercise sets that range in difficulty from basic to challenging. The text should be useful to graduate students in mathematics, physics, and engineering.
| Author | : Nolan R. Wallach |
| Publisher | : Academic Press |
| Total Pages | : 439 |
| Release | : 1988-03-01 |
| Genre | : Mathematics |
| ISBN | : 0080874517 |
Real Reductive Groups I is an introduction to the representation theory of real reductive groups. It is based on courses that the author has given at Rutgers for the past 15 years. It also had its genesis in an attempt of the author to complete a manuscript of the lectures that he gave at the CBMS regional conference at The University of North Carolina at Chapel Hill in June of 1981. This book comprises 10 chapters and begins with some background material as an introduction. The following chapters then discuss elementary representation theory; real reductive groups; the basic theory of (g, K)-modules; the asymptotic behavior of matrix coefficients; The Langlands Classification; a construction of the fundamental series; cusp forms on G; character theory; and unitary representations and (g, K)-cohomology. This book will be of interest to mathematicians and statisticians.
