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Convolution Operators On Groups
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Book Synopsis Convolution Operators on Groups by : Antoine Derighetti
Download or read book Convolution Operators on Groups written by Antoine Derighetti and published by Springer Science & Business Media. This book was released on 2011-06-27 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to a systematic study of the Banach algebra of the convolution operators of a locally compact group. Inspired by classical Fourier analysis we consider operators on Lp spaces, arriving at a description of these operators and Lp versions of the theorems of Wiener and Kaplansky-Helson.
Book Synopsis Matrix Convolution Operators on Groups by : Cho-Ho Chu
Download or read book Matrix Convolution Operators on Groups written by Cho-Ho Chu and published by Springer Science & Business Media. This book was released on 2008-08-25 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents developments in the spectral theory of convolution operators of matrix functions. It studies the contractivity properties of matrix convolution semigroups and details applications to harmonic functions.
Book Synopsis On the spectrum of convolution operators on groups with polynomial growth by : A. Hulanicki
Download or read book On the spectrum of convolution operators on groups with polynomial growth written by A. Hulanicki and published by . This book was released on 1972 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Group convolution operators on standard CR-manifolds by : N. L. Vasilevski
Download or read book Group convolution operators on standard CR-manifolds written by N. L. Vasilevski and published by . This book was released on 1992 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stable Probability Measures on Euclidean Spaces and on Locally Compact Groups by : Wilfried Hazod
Download or read book Stable Probability Measures on Euclidean Spaces and on Locally Compact Groups written by Wilfried Hazod and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalising classical concepts of probability theory, the investigation of operator (semi)-stable laws as possible limit distributions of operator-normalized sums of i.i.d. random variable on finite-dimensional vector space started in 1969. Currently, this theory is still in progress and promises interesting applications. Parallel to this, similar stability concepts for probabilities on groups were developed during recent decades. It turns out that the existence of suitable limit distributions has a strong impact on the structure of both the normalizing automorphisms and the underlying group. Indeed, investigations in limit laws led to contractable groups and - at least within the class of connected groups - to homogeneous groups, in particular to groups that are topologically isomorphic to a vector space. Moreover, it has been shown that (semi)-stable measures on groups have a vector space counterpart and vice versa. The purpose of this book is to describe the structure of limit laws and the limit behaviour of normalized i.i.d. random variables on groups and on finite-dimensional vector spaces from a common point of view. This will also shed a new light on the classical situation. Chapter 1 provides an introduction to stability problems on vector spaces. Chapter II is concerned with parallel investigations for homogeneous groups and in Chapter III the situation beyond homogeneous Lie groups is treated. Throughout, emphasis is laid on the description of features common to the group- and vector space situation. Chapter I can be understood by graduate students with some background knowledge in infinite divisibility. Readers of Chapters II and III are assumed to be familiar with basic techniques from probability theory on locally compact groups.
Book Synopsis Singular Convolution Operators of Hilbert Type on a Class of Totally Disconnected Abelian Groups by : Victor Ndakbo
Download or read book Singular Convolution Operators of Hilbert Type on a Class of Totally Disconnected Abelian Groups written by Victor Ndakbo and published by . This book was released on 1982 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Convolution Operators which are Not of Scalar Type by : G. L. Krabbe
Download or read book Convolution Operators which are Not of Scalar Type written by G. L. Krabbe and published by . This book was released on 1958 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Probability on Compact Lie Groups by : David Applebaum
Download or read book Probability on Compact Lie Groups written by David Applebaum and published by Springer. This book was released on 2014-06-26 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability theory on compact Lie groups deals with the interaction between “chance” and “symmetry,” a beautiful area of mathematics of great interest in its own sake but which is now also finding increasing applications in statistics and engineering (particularly with respect to signal processing). The author gives a comprehensive introduction to some of the principle areas of study, with an emphasis on applicability. The most important topics presented are: the study of measures via the non-commutative Fourier transform, existence and regularity of densities, properties of random walks and convolution semigroups of measures and the statistical problem of deconvolution. The emphasis on compact (rather than general) Lie groups helps readers to get acquainted with what is widely seen as a difficult field but which is also justified by the wealth of interesting results at this level and the importance of these groups for applications. The book is primarily aimed at researchers working in probability, stochastic analysis and harmonic analysis on groups. It will also be of interest to mathematicians working in Lie theory and physicists, statisticians and engineers who are working on related applications. A background in first year graduate level measure theoretic probability and functional analysis is essential; a background in Lie groups and representation theory is certainly helpful but the first two chapters also offer orientation in these subjects.
Book Synopsis Four Short Courses on Harmonic Analysis by : Brigitte Forster
Download or read book Four Short Courses on Harmonic Analysis written by Brigitte Forster and published by Springer Science & Business Media. This book was released on 2010 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by internationally renowned mathematicians, this state-of-the-art textbook examines four research directions in harmonic analysis and features some of the latest applications in the field. The work is the first one that combines spline theory, wavelets, frames, and time-frequency methods leading up to a construction of wavelets on manifolds other than Rn. Four Short Courses on Harmonic Analysis is intended as a graduate-level textbook for courses or seminars on harmonic analysis and its applications. The work is also an excellent reference or self-study guide for researchers and practitioners with diverse mathematical backgrounds working in different fields such as pure and applied mathematics, image and signal processing engineering, mathematical physics, and communication theory.
Book Synopsis Partial Differential and Integral Equations by : Heinrich Begehr
Download or read book Partial Differential and Integral Equations written by Heinrich Begehr and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of the Proceedings of the congress ISAAC '97 collects the con tributions of the four sections 1. Function theoretic and functional analytic methods for pde, 2. Applications of function theory of several complex variables to pde, 3. Integral equations and boundary value problems, 4. Partial differential equations. Most but not all of the authors have participated in the congress. Unfortunately some from Eastern Europe and Asia have not managed to come because of lack of financial support. Nevertheless their manuscripts of the proposed talks are included in this volume. The majority of the papers deal with complex methods. Among them boundary value problems in particular the Riemann-Hilbert, the Riemann (Hilbert) and related problems are treated. Boundary behaviour of vector-valued functions are studied too. The Riemann-Hilbert problem is solved for elliptic complex equations, for mixed complex equations, and for several complex variables. It is considered in a general topological setting for mappings into q;n and related to Toeplitz operators. Convolution operators are investigated for nilpotent Lie groups leading to some consequences for the null space of the tangential Cauchy Riemann operator. Some boundary value problems for overdetermined systems in balls of q;n are solved explicitly. A survey is given for the Gauss-Manin connection associated with deformations of curve singularities. Several papers deal with generalizations of analytic functions with various applications to mathematical physics. Singular integrals in quaternionic anal ysis are studied which are applied to the time-harmonic Maxwell equations.
Book Synopsis Probability Measures on Locally Compact Groups by : H. Heyer
Download or read book Probability Measures on Locally Compact Groups written by H. Heyer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability measures on algebraic-topological structures such as topological semi groups, groups, and vector spaces have become of increasing importance in recent years for probabilists interested in the structural aspects of the theory as well as for analysts aiming at applications within the scope of probability theory. In order to obtain a natural framework for a first systematic presentation of the most developed part of the work done in the field we restrict ourselves to prob ability measures on locally compact groups. At the same time we stress the non Abelian aspect. Thus the book is concerned with a set of problems which can be regarded either from the probabilistic or from the harmonic-analytic point of view. In fact, it seems to be the synthesis of these two viewpoints, the initial inspiration coming from probability and the refined techniques from harmonic analysis which made this newly established subject so fascinating. The goal of the presentation is to give a fairly complete treatment of the central limit problem for probability measures on a locally compact group. In analogy to the classical theory the discussion is centered around the infinitely divisible probability measures on the group and their relationship to the convergence of infinitesimal triangular systems.
Book Synopsis Limit Operators and Their Applications in Operator Theory by : Vladimir Rabinovich
Download or read book Limit Operators and Their Applications in Operator Theory written by Vladimir Rabinovich and published by Birkhäuser. This book was released on 2012-12-06 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first monograph devoted to a fairly wide class of operators, namely band and band-dominated operators and their Fredholm theory. The main tool in studying this topic is limit operators. Applications are presented to several important classes of such operators: convolution type operators and pseudo-differential operators on bad domains and with bad coefficients.
Book Synopsis Multipliers and Convolution Operators with Natural Spectrum on Group Algebras by : Pietro Aiena
Download or read book Multipliers and Convolution Operators with Natural Spectrum on Group Algebras written by Pietro Aiena and published by . This book was released on 1992 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fourier Analysis on Finite Groups with Applications in Signal Processing and System Design by : Radomir S. Stankovic
Download or read book Fourier Analysis on Finite Groups with Applications in Signal Processing and System Design written by Radomir S. Stankovic and published by John Wiley & Sons. This book was released on 2005-08-08 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover applications of Fourier analysis on finite non-Abeliangroups The majority of publications in spectral techniques considerFourier transform on Abelian groups. However, non-Abelian groupsprovide notable advantages in efficient implementations of spectralmethods. Fourier Analysis on Finite Groups with Applications in SignalProcessing and System Design examines aspects of Fourieranalysis on finite non-Abelian groups and discusses differentmethods used to determine compact representations for discretefunctions providing for their efficient realizations and relatedapplications. Switching functions are included as an example ofdiscrete functions in engineering practice. Additionally,consideration is given to the polynomial expressions and decisiondiagrams defined in terms of Fourier transform on finitenon-Abelian groups. A solid foundation of this complex topic is provided bybeginning with a review of signals and their mathematical modelsand Fourier analysis. Next, the book examines recent achievementsand discoveries in: Matrix interpretation of the fast Fourier transform Optimization of decision diagrams Functional expressions on quaternion groups Gibbs derivatives on finite groups Linear systems on finite non-Abelian groups Hilbert transform on finite groups Among the highlights is an in-depth coverage of applications ofabstract harmonic analysis on finite non-Abelian groups in compactrepresentations of discrete functions and related tasks in signalprocessing and system design, including logic design. All chaptersare self-contained, each with a list of references to facilitatethe development of specialized courses or self-study. With nearly 100 illustrative figures and fifty tables, this isan excellent textbook for graduate-level students and researchersin signal processing, logic design, and system theory-as well asthe more general topics of computer science and appliedmathematics.
Book Synopsis Fourier and Fourier-Stieltjes Algebras on Locally Compact Groups by : Eberhard Kaniuth
Download or read book Fourier and Fourier-Stieltjes Algebras on Locally Compact Groups written by Eberhard Kaniuth and published by American Mathematical Soc.. This book was released on 2018-07-05 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of the Fourier algebra lies at the crossroads of several areas of analysis. Its roots are in locally compact groups and group representations, but it requires a considerable amount of functional analysis, mainly Banach algebras. In recent years it has made a major connection to the subject of operator spaces, to the enrichment of both. In this book two leading experts provide a road map to roughly 50 years of research detailing the role that the Fourier and Fourier-Stieltjes algebras have played in not only helping to better understand the nature of locally compact groups, but also in building bridges between abstract harmonic analysis, Banach algebras, and operator algebras. All of the important topics have been included, which makes this book a comprehensive survey of the field as it currently exists. Since the book is, in part, aimed at graduate students, the authors offer complete and readable proofs of all results. The book will be well received by the community in abstract harmonic analysis and will be particularly useful for doctoral and postdoctoral mathematicians conducting research in this important and vibrant area.
Book Synopsis Harmonic Analysis on Free Groups by : Alessandro Figa-Talamanca
Download or read book Harmonic Analysis on Free Groups written by Alessandro Figa-Talamanca and published by CRC Press. This book was released on 2020-11-26 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an account of recent results on the theory of representations and the harmonic analysis of free groups. It emphasizes the analogy with the theory of representations of noncompact semisimple Lie groups and restricts the focus to a class of irreducible unitary representations.
Book Synopsis Pseudo-Differential Operators and Symmetries by : Michael V. Ruzhansky
Download or read book Pseudo-Differential Operators and Symmetries written by Michael V. Ruzhansky and published by Springer Science & Business Media. This book was released on 2009-10-19 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the development of the theory of pseudo-di?erential n operators on spaces with symmetries. Such spaces are the Euclidean space R ,the n torus T , compact Lie groups and compact homogeneous spaces. The book consists of several parts. One of our aims has been not only to present new results on pseudo-di?erential operators but also to show parallels between di?erent approaches to pseudo-di?erential operators on di?erent spaces. Moreover, we tried to present the material in a self-contained way to make it accessible for readers approaching the material for the ?rst time. However, di?erent spaces on which we develop the theory of pseudo-di?er- tial operators require di?erent backgrounds. Thus, while operators on the - clidean space in Chapter 2 rely on the well-known Euclidean Fourier analysis, pseudo-di?erentialoperatorsonthetorusandmoregeneralLiegroupsinChapters 4 and 10 require certain backgrounds in discrete analysis and in the representation theory of compact Lie groups, which we therefore present in Chapter 3 and in Part III,respectively. Moreover,anyonewhowishestoworkwithpseudo-di?erential- erators on Lie groups will certainly bene?t from a good grasp of certain aspects of representation theory. That is why we present the main elements of this theory in Part III, thus eliminating the necessity for the reader to consult other sources for most of the time. Similarly, the backgrounds for the theory of pseudo-di?erential 3 operators on S and SU(2) developed in Chapter 12 can be found in Chapter 11 presented in a self-contained way suitable for immediate use.
