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Commutative And Noncommutative Harmonic Analysis And Applications
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Book Synopsis Engineering Applications of Noncommutative Harmonic Analysis by : Gregory S. Chirikjian
Download or read book Engineering Applications of Noncommutative Harmonic Analysis written by Gregory S. Chirikjian and published by CRC Press. This book was released on 2000-09-28 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Commutative and Noncommutative Harmonic Analysis and Applications by : Azita Mayeli
Download or read book Commutative and Noncommutative Harmonic Analysis and Applications written by Azita Mayeli and published by American Mathematical Soc.. This book was released on 2013-11-08 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Non-commutative Analysis by : Palle Jorgensen
Download or read book Non-commutative Analysis written by Palle Jorgensen and published by World Scientific. This book was released on 2017-01-24 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: '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.
Book Synopsis Noncommutative Geometry by : Alain Connes
Download or read book Noncommutative Geometry written by Alain Connes and published by Springer. This book was released on 2003-12-15 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.
Book Synopsis Free Random Variables by : Dan V. Voiculescu
Download or read book Free Random Variables written by Dan V. Voiculescu and published by American Mathematical Soc.. This book was released on 1992 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Noncommutative Microlocal Analysis by : Michael Eugene Taylor
Download or read book Noncommutative Microlocal Analysis written by Michael Eugene Taylor and published by American Mathematical Soc.. This book was released on 1984 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Non-Commutative Harmonic Analysis by : Raymond C. Fabec
Download or read book Non-Commutative Harmonic Analysis written by Raymond C. Fabec and published by . This book was released on 2014-07-06 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Explorations in Harmonic Analysis by : Steven G. Krantz
Download or read book Explorations in Harmonic Analysis written by Steven G. Krantz and published by Springer Science & Business Media. This book was released on 2009-05-24 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis.
Book Synopsis The Scope and History of Commutative and Noncommutative Harmonic Analysis by : George W. Mackey
Download or read book The Scope and History of Commutative and Noncommutative Harmonic Analysis written by George W. Mackey and published by American Mathematical Soc.. This book was released on 2005-04-08 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: ''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.
Book Synopsis Quantum Harmonic Analysis by : Maurice A. de Gosson
Download or read book Quantum Harmonic Analysis written by Maurice A. de Gosson and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-07-05 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics is arguably one of the most successful scientific theories ever and its applications to chemistry, optics, and information theory are innumerable. This book provides the reader with a rigorous treatment of the main mathematical tools from harmonic analysis which play an essential role in the modern formulation of quantum mechanics. This allows us at the same time to suggest some new ideas and methods, with a special focus on topics such as the Wigner phase space formalism and its applications to the theory of the density operator and its entanglement properties. This book can be used with profit by advanced undergraduate students in mathematics and physics, as well as by confirmed researchers.
Book Synopsis Fourier Analysis on Finite Groups and Applications by : Audrey Terras
Download or read book Fourier Analysis on Finite Groups and Applications written by Audrey Terras and published by Cambridge University Press. This book was released on 1999-03-28 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: It examines the theory of finite groups in a manner that is both accessible to the beginner and suitable for graduate research.
Book Synopsis Noncommutative Geometry, Quantum Fields and Motives by : Alain Connes
Download or read book Noncommutative Geometry, Quantum Fields and Motives written by Alain Connes and published by American Mathematical Soc.. This book was released on 2019-03-13 with total page 810 pages. Available in PDF, EPUB and Kindle. Book excerpt: The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book deals with quantum field theory and the geometric structure of renormalization as a Riemann-Hilbert correspondence. It also presents a model of elementary particle physics based on noncommutative geometry. The main result is a complete derivation of the full Standard Model Lagrangian from a very simple mathematical input. Other topics covered in the first part of the book are a noncommutative geometry model of dimensional regularization and its role in anomaly computations, and a brief introduction to motives and their conjectural relation to quantum field theory. The second part of the book gives an interpretation of the Weil explicit formula as a trace formula and a spectral realization of the zeros of the Riemann zeta function. This is based on the noncommutative geometry of the adèle class space, which is also described as the space of commensurability classes of Q-lattices, and is dual to a noncommutative motive (endomotive) whose cyclic homology provides a general setting for spectral realizations of zeros of L-functions. The quantum statistical mechanics of the space of Q-lattices, in one and two dimensions, exhibits spontaneous symmetry breaking. In the low-temperature regime, the equilibrium states of the corresponding systems are related to points of classical moduli spaces and the symmetries to the class field theory of the field of rational numbers and of imaginary quadratic fields, as well as to the automorphisms of the field of modular functions. The book ends with a set of analogies between the noncommutative geometries underlying the mathematical formulation of the Standard Model minimally coupled to gravity and the moduli spaces of Q-lattices used in the study of the zeta function.
Book Synopsis Commutative Normed Rings by : Izrailʹ Moiseevich Gelʹfand
Download or read book Commutative Normed Rings written by Izrailʹ Moiseevich Gelʹfand and published by Taylor & Francis US. This book was released on 1999 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the Preface (1960): "This book is devoted to an account of one of the branches of functional analysis, the theory of commutative normed rings, and the principal applications of that theory. It is based on [the authors'] paper written ... in 1940, hard on the heels of the initial period of the development of this theory ... "The book consists of three parts. Part one, concerned with the theory of commutative normed rings and divided into two chapters; the first containing foundations of the theory and the second dealing with more special problems. Part two deals with applications to harmonic analysis and is divided into three chapters. The first chapter discusses the ring of absolutely integrable functions on a line with convolution as multiplication and finds the maximal ideals of this ring and some of its analogues. In the next chapter, these results are carried over to arbitrary commutative locally compact groups and they are made the foundation of the construction of harmonic analysis and the theory of characters. A new feature here is the construction of an invariant measure on the group of characters and a proof of the inversion formula for Fourier transforms that is not based on theorems on the representation of positive-definite functions or positive functionals ... The last chapter of the second part--the most specialized of all the chapters--is devoted to the investigation of the ring of functions of bounded variation on a line with multiplication defined as convolution, including the complete description of the maximal ideals of this ring. The third part of the book is devoted to the discussion of two important classes of rings of functions: regular rings and rings with uniform convergence. The first of the chapters essentially studies the structure of ideals in regular rings. The chapter ends with an example of a ring of functions having closed ideals that cannot be represented as the intersections of maximal ideals. The second chapter discusses the ring C(S) of all bounded continuous complex functions on completely regular spaces S and various of its subrings ... "Since noncommutative normed rings with an involution are important for group-theoretical applications, the paper by I. M. Gelfand and N. A. Naimark, `Normed Rings with an Involution and their Representations', is reproduced at the end of the book, slightly abridged, in the form of an appendix ... This monograph also contains an account of the foundations of the theory of commutative normed rings without, however, touching upon the majority of its analytic applications ... "The reader [should] have knowledge of the elements of the theory of normed spaces and of set-theoretical topology. For an understanding of the fourth chapter, [the reader should] also know what a topological group is. It stands to reason that the basic concepts of the theory of measure and of the Lebesgue integral are also assumed to be known ... "
Book Synopsis High-Dimensional Probability by : Roman Vershynin
Download or read book High-Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Book Synopsis Introduction to Matrix Analysis and Applications by : Fumio Hiai
Download or read book Introduction to Matrix Analysis and Applications written by Fumio Hiai and published by Springer Science & Business Media. This book was released on 2014-02-06 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrices can be studied in different ways. They are a linear algebraic structure and have a topological/analytical aspect (for example, the normed space of matrices) and they also carry an order structure that is induced by positive semidefinite matrices. The interplay of these closely related structures is an essential feature of matrix analysis. This book explains these aspects of matrix analysis from a functional analysis point of view. After an introduction to matrices and functional analysis, it covers more advanced topics such as matrix monotone functions, matrix means, majorization and entropies. Several applications to quantum information are also included. Introduction to Matrix Analysis and Applications is appropriate for an advanced graduate course on matrix analysis, particularly aimed at studying quantum information. It can also be used as a reference for researchers in quantum information, statistics, engineering and economics.
Book Synopsis Geometric Models for Noncommutative Algebras by : Ana Cannas da Silva
Download or read book Geometric Models for Noncommutative Algebras written by Ana Cannas da Silva and published by American Mathematical Soc.. This book was released on 1999 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume is based on a course, ``Geometric Models for Noncommutative Algebras'' taught by Professor Weinstein at Berkeley. Noncommutative geometry is the study of noncommutative algebras as if they were algebras of functions on spaces, for example, the commutative algebras associated to affine algebraic varieties, differentiable manifolds, topological spaces, and measure spaces. In this work, the authors discuss several types of geometric objects (in the usual sense of sets with structure) that are closely related to noncommutative algebras. Central to the discussion are symplectic and Poisson manifolds, which arise when noncommutative algebras are obtained by deforming commutative algebras. The authors also give a detailed study of groupoids (whose role in noncommutative geometry has been stressed by Connes) as well as of Lie algebroids, the infinitesimal approximations to differentiable groupoids. Featured are many interesting examples, applications, and exercises. The book starts with basic definitions and builds to (still) open questions. It is suitable for use as a graduate text. An extensive bibliography and index are included.
Book Synopsis Engineering Applications of Noncommutative Harmonic Analysis by : Gregory S. Chirikjian
Download or read book Engineering Applications of Noncommutative Harmonic Analysis written by Gregory S. Chirikjian and published by CRC Press. This book was released on 2021-02-25 with total page 697 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
