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Author : Marek Bożejko,Anna Krystek,Łukasz Wojakowski
Publisher : Unknown
Page : 317 pages
File Size : 40,6 Mb
Release : 2012
Category : Free probability theory
ISBN : 838680615X
Author : Marek Bożejko
Publisher : Unknown
Page : 334 pages
File Size : 54,6 Mb
Release : 2007
Category : Free probability theory
ISBN : UOM:39015075633761
Author : Marek Bożejko
Publisher : Unknown
Page : 327 pages
File Size : 50,9 Mb
Release : 2010
Category : Free probability theory
ISBN : OCLC:805032778
Author : Dan V. Voiculescu,K. J. Dykema,A. Nica
Publisher : American Mathematical Soc.
Page : 80 pages
File Size : 44,6 Mb
Release : 1992
Category : Mathematics
ISBN : 9780821811405
This book presents the first comprehensive introduction to free probability theory, a highly noncommutative probability theory with independence based on free products instead of tensor products. Basic examples of this kind of theory are provided by convolution operators on free groups and by the asymptotic behavior of large Gaussian random matrices. The probabilistic approach to free products has led to a recent surge of new results on the von Neumann algebras of free groups. The book is ideally suited as a textbook for an advanced graduate course and could also provide material for a seminar. In addition to researchers and graduate students in mathematics, this book will be of interest to physicists and others who use random matrices.
Author : Dan V. Voiculescu
Publisher : Unknown
Page : 70 pages
File Size : 51,9 Mb
Release : 1992
Category : Free products
ISBN : 147043847X
This book presents the first comprehensive introduction to free probability theory, a highly noncommutative probability theory with independence based on free products instead of tensor products. Basic examples of this kind of theory are provided by convolution operators on free groups and by the asymptotic behavior of large Gaussian random matrices. The probabilistic approach to free products has led to a recent surge of new results on the von Neumann algebras of free groups. The book is ideally suited as a textbook for an advanced graduate course and could also provide material for a seminar.
Author : Michael Eugene Taylor
Publisher : American Mathematical Soc.
Page : 328 pages
File Size : 55,8 Mb
Release : 1986
Category : Mathematics
ISBN : 9780821815236
This book 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. It began as lecture notes for a one-semester graduate course given by the author in noncommutative harmonic analysis. It is a valuable resource for both graduate students and faculty, and requires only a background with Fourier analysis and basic functional analysis, plus the first few chapters of a standard text on Lie groups. The basic method of noncommutative harmonic analysis, a generalization of Fourier analysis, is to synthesize operators on a space on which a Lie group has a unitary representation from operators on irreducible representation spaces.Though the general study is far from complete, this book covers a great deal of the progress that has been made on important classes of Lie groups. Unlike many other books on harmonic analysis, this book focuses on the relationship between harmonic analysis and partial differential equations. The author considers many classical PDEs, particularly boundary value problems for domains with simple shapes, that exhibit noncommutative groups of symmetries. Also, the book contains detailed work, which has not previously been published, on the harmonic analysis of the Heisenberg group and harmonic analysis on cones.
Author : Azita Mayeli
Publisher : American Mathematical Soc.
Page : 218 pages
File Size : 47,9 Mb
Release : 2013-11-08
Category : Mathematics
ISBN : 9780821894934
This volume contains the proceedings of the AMS Special Session on Wavelet and Frame Theoretic Methods in Harmonic Analysis and Partial Differential Equations, held September 22-23, 2012, at the Rochester Institute of Technology, Rochester, NY, USA. The book features new directions, results and ideas in commutative and noncommutative abstract harmonic analysis, operator theory and applications. The commutative part includes shift invariant spaces, abelian group action on Euclidean space and frame theory; the noncommutative part includes representation theory, continuous and discrete wavelets related to four dimensional Euclidean space, frames on symmetric spaces, $C DEGREES*$-algebras, projective multiresolutions, and free probability algebras. The scope of the book goes beyond traditional harmonic analysis, dealing with Fourier tools, transforms, Fourier bases, and associated function spaces. A number of papers take the step toward wavelet analysis, and even more general tools for analysis/synthesis problems, including papers on frames (over-complete bases) and their practical applications to engineering, cosmology and astrophysics.Other applications in this book include explicit families of wavelets and frames, as they are used in signal processing, multiplexing, and the study of Cosmic Microwave Background (CMB) radiation. For the purpose of organisation, the book is divided into three parts: noncommutative, commutative, and applications. The first group of papers are devoted to problems in noncommutative harmonic analysis, the second to topics in commutative harmonic analysis, and the third to such applications as wavelet and frame theory and to some real-world applications.
Author : Carlos E. Kenig
Publisher : American Mathematical Soc.
Page : 345 pages
File Size : 52,5 Mb
Release : 2020-12-14
Category : Education
ISBN : 9781470461270
The origins of the harmonic analysis go back to an ingenious idea of Fourier that any reasonable function can be represented as an infinite linear combination of sines and cosines. Today's harmonic analysis incorporates the elements of geometric measure theory, number theory, probability, and has countless applications from data analysis to image recognition and from the study of sound and vibrations to the cutting edge of contemporary physics. The present volume is based on lectures presented at the summer school on Harmonic Analysis. These notes give fresh, concise, and high-level introductions to recent developments in the field, often with new arguments not found elsewhere. The volume will be of use both to graduate students seeking to enter the field and to senior researchers wishing to keep up with current developments.
Author : Saloman Bochner
Publisher : Univ of California Press
Page : 184 pages
File Size : 51,9 Mb
Release : 2023-11-15
Category : Mathematics
ISBN : 9780520345294
This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1955.
Author : Jorgensen Palle,Tian Feng
Publisher : World Scientific
Page : 564 pages
File Size : 55,8 Mb
Release : 2017-01-24
Category : Mathematics
ISBN : 9789813202146
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 : Salomon Bochner
Publisher : Courier Corporation
Page : 190 pages
File Size : 55,9 Mb
Release : 2013-11-07
Category : Mathematics
ISBN : 9780486154800
Written by a distinguished mathematician and educator, this classic text emphasizes stochastic processes and the interchange of stimuli between probability and analysis. It also introduces the author's innovative concept of the characteristic functional. 1955 edition.
Author : J. Carmona,M. Vergne
Publisher : Springer
Page : 249 pages
File Size : 49,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540373650
Author : Gregory S. Chirikjian,Alexander B. Kyatkin
Publisher : CRC Press
Page : 697 pages
File Size : 45,8 Mb
Release : 2021-02-25
Category : Mathematics
ISBN : 9781000694253
First published in 2001. 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 still no place they can turn to for a clear presentation of the background they need to apply the concept to engineering problems. Engineering Applications of Noncommutative Harmonic Analysis brings this powerful tool to the engineering world. Written specifically for engineers and computer scientists, it offers a practical treatment of harmonic analysis in the context of particular Lie groups (rotation and Euclidean motion). It presents only a limited number of proofs, focusing instead on providing a review of the fundamental mathematical results unknown to most engineers and detailed discussions of specific applications. Advances in pure mathematics can lead to very tangible advances in engineering, but only if they are available and accessible to engineers. Engineering Applications of Noncommutative Harmonic Analysis provides the means for adding this valuable and effective technique to the engineer's toolbox.
Author : George W. Mackey
Publisher : American Mathematical Soc.
Page : 386 pages
File Size : 47,9 Mb
Release : 2005-04-08
Category : Mathematics
ISBN : 0821890441
''When I was invited to speak at the conference on the history of analysis given at Rice University [in 1977], I decided that it might be interesting to review the history of mathematics and physics in the last three hundred years or so with heavy emphasis on those parts in which harmonic analysis had played a decisive or at least a major role. I was pleased and somewhat astonished to find how much of both subjects could be included under this rubric ... The picture that gradually emerged as the various details fell into place was one that I found very beautiful, and the process of seeing it do so left me in an almost constant state of euphoria. I would like to believe that others can be led to see this picture by reading my paper, and to facilitate this I have included a large number of short expositions of topics which are not widely understood by non-specialists.'' --from the Preface This volume, containing the paper mentioned above as well as five other reprinted papers by Mackey, presents a sweeping view of the importance, utility, and beauty of harmonic analysis and its connections to other areas of mathematics and science. A seventh paper, written exclusively for this volume, attempts to unify certain themes that emerged after major discoveries in 1967 and 1968 in the areas of Lie algebras, strong interaction physics, statistical mechanics, and nonlinear partial differential equations--discoveries that may at first glance appear to be independent, but which are in fact deeply interrelated. Information for our distributors: Copublished with the London Mathematical Society beginning with volume 4. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners.
Author : Michael E. Taylor
Publisher : American Mathematical Society(RI)
Page : 0 pages
File Size : 55,9 Mb
Release : 1986
Category : Harmonic analysis
ISBN : 1470412497
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.