Bøger i Applied and Numerical Harmonic Analysis serien

Describing novel mathematical concepts for recommendation engines, Realtime Data Mining: Self-Learning Techniques for Recommendation Engines features a sound mathematical framework unifying approaches based on control and learning theories, tensor factorization, and hierarchical methods.

The chapters of this volume are based on talks given at the eleventh international Sampling Theory and Applications conference held in 2015 at American University in Washington, D.C. The papers highlight state-of-the-art advances and trends in sampling theory and related areas of application, such as signal and image processing. Chapters have been written by prominent mathematicians, applied scientists, and engineers with an expertise in sampling theory. Claude Shannon¿s 100th birthday is also celebrated, including an introductory essay that highlights Shannon¿s profound influence on the field. The topics covered include both theory and applications, such as:¿ Compressed sensing¿ Non-uniform and wave sampling¿ A-to-D conversion¿ Finite rate of innovation¿ Time-frequency analysis¿ Operator theory¿ Mobile sampling issuesSampling: Theory and Applications is ideal for mathematicians, engineers, and applied scientists working in sampling theory or related areas.

This monograph introduces a novel and effective approach to counting lattice paths by using the discrete Fourier transform (DFT) as a type of periodic generating function.

This book investigates the convergence and summability of both one-dimensional and multi-dimensional Fourier transforms, as well as the theory of Hardy spaces.

Different aspects of harmonic analysis, complex analysis, sampling theory, approximation theory and related topics are covered in this volume.

The chapters in this volume are based on talks given at the inaugural Aspects of Time-Frequency Analysis conference held in Turin, Italy from July 5-7, 2017, which brought together experts in harmonic analysis and its applications.

Moreover, it brings to light new interrelations between these functions and the real Hardy space and, correspondingly, between the Fourier transform and the Hilbert transform. In turn, the second part examines the Fourier transforms of multivariate functions with bounded Hardy variation.

This book provides an accessible introduction to the theory of variable Lebesgue spaces. These spaces generalize the classical Lebesgue spaces by replacing the constant exponent p with a variable exponent p(x). They were introduced in the early 1930s but have become the focus of renewed interest since the early 1990s because of their connection with the calculus of variations and partial differential equations with nonstandard growth conditions, and for their applications to problems in physics and image processing. The book begins with the development of the basic function space properties. It avoids a more abstract, functional analysis approach, instead emphasizing an hands-on approach that makes clear the similarities and differences between the variable and classical Lebesgue spaces. The subsequent chapters are devoted to harmonic analysis on variable Lebesgue spaces. The theory of the Hardy-Littlewood maximal operator is completely developed, and the connections between variable Lebesgue spaces and the weighted norm inequalities are introduced. The other important operators in harmonic analysis - singular integrals, Riesz potentials, and approximate identities - are treated using a powerful generalization of the Rubio de Francia theory of extrapolation from the theory of weighted norm inequalities. The final chapter applies the results from previous chapters to prove basic results about variable Sobolev spaces.

This textbook acts as a pathway to higher mathematics by seeking and illuminating the connections between graph theory and diverse fields of mathematics, such as calculus on manifolds, group theory, algebraic curves, Fourier analysis, cryptography and other areas of combinatorics.

This volume, a collection of invited contributions developed from talks at an international conference on wavelets, is divided into three parts: Part I is devoted to the mathematical theory of wavelets and features several papers on wavelet sets and the construction of wavelet bases in different settings.

Since publication of the initial papers in 2006, compressed sensing has captured the imagination of the international signal processing community, and the mathematical foundations are nowadays quite well understood.Parallel to the progress in mathematics, the potential applications of compressed sensing have been explored by many international groups of, in particular, engineers and applied mathematicians, achieving very promising advances in various areas such as communication theory, imaging sciences, optics, radar technology, sensor networks, or tomography.Since many applications have reached a mature state, the research center MATHEON in Berlin focusing on "Mathematics for Key Technologies", invited leading researchers on applications of compressed sensing from mathematics, computer science, and engineering to the "MATHEON Workshop 2013: Compressed Sensing and its Applications¿ in December 2013. It was the first workshop specifically focusing on the applications of compressed sensing. This book features contributions by the plenary and invited speakers of this workshop. To make this book accessible for those unfamiliar with compressed sensing, the book will not only contain chapters on various applications of compressed sensing written by plenary and invited speakers, but will also provide a general introduction into compressed sensing.The book is aimed at both graduate students and researchers in the areas of applied mathematics, computer science, and engineering as well as other applied scientists interested in the potential and applications of the novel methodology of compressed sensing. For those readers who are not already familiar with compressed sensing, an introduction to the basics of this theory will be included.

Time-frequency analysis is a modern branch of harmonic analysis. The topics range from the elemen tary theory of the short-time Fourier transform and classical results about the Wigner distribution via the recent theory of Gabor frames to quantita tive methods in time-frequency analysis and the theory of pseudodifferential operators.

This book presents connections between the different aspects of wavelet and subband theory.

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 Norbert Wiener Center for Harmonic Analysis and Applications provides a state-of-the-art research venue for the broad emerging area of mathematical engineering in the context of harmonic analysis.

The 7th International Workshop in Analysis and its Applications (IWAA) was held at the University of Maine, June 1-6, 1997 and featured approxi mately 60 mathematicians. The principal theme for the fourth meeting (June 1-10, 1990, Kupuri) was Inner Product and Convexity Structures in Analysis, Mathematical Physics, and Economics.

The Norbert Wiener Center for Harmonic Analysis and Applications provides a state-of-the-art research venue for the broad emerging area of mathematical engineering in the context of harmonic analysis.

This volume consists of contributions spanning a wide spectrum of harmonic analysis and its applications written by speakers at the February Fourier Talks from 2002 - 2013.

The idea of this book originated in the works presented at the First Latinamerican Conference on Mathematics in Industry and Medicine, held in Buenos Aires, Argentina, from November 27 to December 1, 1995. There are excellent introductions already available, for example, Chapter one in Wavelets in Medicine and Biology, edited by A.

This book presents connections between the different aspects of wavelet and subband theory.

The growing need to efficiently obtain precise and tailored digital representations of complex objects and phenomena requires the maturation of available tools in Sampling Theory as well as the development of complementary, novel mathematical theories.

His sphere of influence ranges from purely theoretical results regarding the representations of locally compact groups to recent applications of wavelets and frames to problems in sampling theory and image compression.

A comprehensive exposition on analytic methods for solving science and engineering problems, written from the unifying viewpoint of distribution theory and enriched with many modern topics which are important to practioners and researchers. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise.

This book explore the use of new technologies in the area of satellite navigation receivers. In order to construct a reconfigurable receiver with a wide range of applications, the authors discuss receiver architecture based on software-defined radio techniques.

Time-frequency analysis is a modern branch of harmonic analysis. The topics range from the elemen tary theory of the short-time Fourier transform and classical results about the Wigner distribution via the recent theory of Gabor frames to quantita tive methods in time-frequency analysis and the theory of pseudodifferential operators.

This concisely written book gives an elementary introduction to a classical area of mathematics - approximation theory - in a way that naturally leads to the modern field of wavelets.

This text is a self-contained introduction to the three main families that we encounter in analysis - metric spaces, normed spaces, and inner product spaces - and to the operators that transform objects in one into objects in another.

In this set of lecture notes, the author includes some of the latest research on the theory of Morrey Spaces associated with Harmonic Analysis.

The theory and applications of finite tight frames has developed rapidly in recent years. This text offers an overview of the field and discusses future research directions. It includes exercises, MATLAB examples for classroom use, and numerous illustrations.

This book provides an introduction to discrete harmonic analysis (DHA) with a view towards applications to digital signal processing.