A Modern Approach to Functional Integration

Author: John R. Klauder

Publisher: Springer Science & Business Media

ISBN: 0817647902

Category: Mathematics

Page: 282

View: 2697

This text takes advantage of recent developments in the theory of path integration and attempts to make a major paradigm shift in how the art of functional integration is practiced. The techniques developed in the work will prove valuable to graduate students and researchers in physics, chemistry, mathematical physics, and applied mathematics who find it necessary to deal with solutions to wave equations, both quantum and beyond. A Modern Approach to Functional Integration offers insight into a number of contemporary research topics, which may lead to improved methods and results that cannot be found elsewhere in the textbook literature. Exercises are included in most chapters, making the book suitable for a one-semester graduate course on functional integration.

Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science

Novel Methods in Harmonic Analysis

Author: Isaac Pesenson,Quoc Thong Le Gia,Azita Mayeli,Hrushikesh Mhaskar,Ding-Xuan Zhou

Publisher: Birkhäuser

ISBN: 3319555561

Category: Mathematics

Page: 510

View: 2247

The second of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume II is organized around the theme of recent applications of harmonic analysis to function spaces, differential equations, and data science, covering topics such as: The classical Fourier transform, the non-linear Fourier transform (FBI transform), cardinal sampling series and translation invariant linear systems. Recent results concerning harmonic analysis on non-Euclidean spaces such as graphs and partially ordered sets. Applications of harmonic analysis to data science and statistics Boundary-value problems for PDE's including the Runge–Walsh theorem for the oblique derivative problem of physical geodesy.

Harmonic and Applied Analysis

From Groups to Signals

Author: Stephan Dahlke,Filippo De Mari,Philipp Grohs,Demetrio Labate

Publisher: Birkhäuser

ISBN: 3319188631

Category: Mathematics

Page: 256

View: 8896

This contributed volume explores the connection between the theoretical aspects of harmonic analysis and the construction of advanced multiscale representations that have emerged in signal and image processing. It highlights some of the most promising mathematical developments in harmonic analysis in the last decade brought about by the interplay among different areas of abstract and applied mathematics. This intertwining of ideas is considered starting from the theory of unitary group representations and leading to the construction of very efficient schemes for the analysis of multidimensional data. After an introductory chapter surveying the scientific significance of classical and more advanced multiscale methods, chapters cover such topics as An overview of Lie theory focused on common applications in signal analysis, including the wavelet representation of the affine group, the Schrödinger representation of the Heisenberg group, and the metaplectic representation of the symplectic group An introduction to coorbit theory and how it can be combined with the shearlet transform to establish shearlet coorbit spaces Microlocal properties of the shearlet transform and its ability to provide a precise geometric characterization of edges and interface boundaries in images and other multidimensional data Mathematical techniques to construct optimal data representations for a number of signal types, with a focus on the optimal approximation of functions governed by anisotropic singularities. A unified notation is used across all of the chapters to ensure consistency of the mathematical material presented. Harmonic and Applied Analysis: From Groups to Signals is aimed at graduate students and researchers in the areas of harmonic analysis and applied mathematics, as well as at other applied scientists interested in representations of multidimensional data. It can also be used as a textbook for graduate courses in applied harmonic analysis.​

Numerical Fourier Analysis

Author: Gerlind Plonka,Daniel Potts,Gabriele Steidl,Manfred Tasche

Publisher: Springer

ISBN: 3030043061

Category: Mathematics

Page: 618

View: 3203

This book offers a unified presentation of Fourier theory and corresponding algorithms emerging from new developments in function approximation using Fourier methods. It starts with a detailed discussion of classical Fourier theory to enable readers to grasp the construction and analysis of advanced fast Fourier algorithms introduced in the second part, such as nonequispaced and sparse FFTs in higher dimensions. Lastly, it contains a selection of numerical applications, including recent research results on nonlinear function approximation by exponential sums. The code of most of the presented algorithms is available in the authors’ public domain software packages. Students and researchers alike benefit from this unified presentation of Fourier theory and corresponding algorithms.

The Journal of NIH Research

Life Sciences Research and News about the National Institutes of Health and the Alcohol, Drug Abuse, and Mental Health Administration

Author: N.A

Publisher: N.A


Category: Medicine

Page: N.A

View: 2063

The Evolution of Applied Harmonic Analysis

Models of the Real World

Author: Elena Prestini

Publisher: Springer Science & Business Media

ISBN: 9780817641252

Category: Mathematics

Page: 351

View: 1774

A sweeping exploration of essential concepts and applications in modern mathematics and science through the unifying framework of Fourier analysis! This unique, extensively illustrated book, accessible to specialists and non-specialists, describes the evolution of harmonic analysis, integrating theory and applications in a way that requires only some general mathematical sophistication and knowledge of calculus in certain sections. Historical sections interwoven with key scientific developments show how, when, where, and why harmonic analysis evolved "The Evolution of Applied Harmonic Analysis" will engage graduate and advanced undergraduate students, researchers, and practitioners in the physical and life sciences, engineering, and mathematics.

An Introduction to Frames and Riesz Bases

Author: Ole Christensen

Publisher: Springer Science & Business Media

ISBN: 9780817642952

Category: Mathematics

Page: 440

View: 7335

The Applied and Numerical Harmonic Analysis ( ANHA) book series aims to provide the engineering, mathematical, and scientific communities with significant developments in harmonic analysis, ranging from abstract har monic analysis to basic applications. The title of the series reflects the im portance of applications and numerical implementation, but richness and relevance of applications and implementation depend fundamentally on the structure and depth of theoretical underpinnings. Thus, from our point of view, the interleaving of theory and applications and their creative symbi otic evolution is axiomatic. Harmonic analysis is a wellspring of ideas and applicability that has flour ished, developed, and deepened over time within many disciplines and by means of creative cross-fertilization with diverse areas. The intricate and fundamental relationship between harmonic analysis and fields such as sig nal processing, partial differential equations (PDEs), and image processing is reflected in our state of the art ANHA series. Our vision of modern harmonic analysis includes mathematical areas such as wavelet theory, Banach algebras, classical Fourier analysis, time frequency analysis, and fractal geometry, as well as the diverse topics that impinge on them.

Advanced Linear Algebra

Author: Steven Roman

Publisher: Springer Science & Business Media

ISBN: 0387728317

Category: Mathematics

Page: 525

View: 1029

This graduate level textbook covers an especially broad range of topics. The book first offers a careful discussion of the basics of linear algebra. It then proceeds to a discussion of modules, emphasizing a comparison with vector spaces, and presents a thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory, culminating in the finite dimensional spectral theorem for normal operators. The new edition has been revised and contains a chapter on the QR decomposition, singular values and pseudoinverses, and a chapter on convexity, separation and positive solutions to linear systems.

An Introduction to Wavelet Analysis

Author: David F. Walnut

Publisher: Springer Science & Business Media

ISBN: 9780817639624

Category: Computers

Page: 449

View: 6330

"An Introduction to Wavelet Analysis provides a comprehensive presentation of the conceptual basis of wavelet analysis, including the construction and application of wavelet bases.

Stochastic Models, Information Theory, and Lie Groups, Volume 2

Analytic Methods and Modern Applications

Author: Gregory S. Chirikjian

Publisher: Springer Science & Business Media

ISBN: 0817649433

Category: Mathematics

Page: 435

View: 8733

This two-volume set covers stochastic processes, information theory and Lie groups in a unified setting, bridging topics rarely studied together. The emphasis is on using stochastic, geometric, and group-theoretic concepts for modeling physical phenomena.

AFOSR Research: the Current Research Program, and a Summary of Research Accomplishments

Author: United States. Air Force. Office of Scientific Research

Publisher: N.A


Category: Research

Page: 231

View: 3552

This report is designed to present the research programs of the Air Force Office of Scientific Research for the information of users of Air Force research, for scientific investigators working in the same or in allied fields, and for the military, scientific and academic, and Government communities at large.


A Classified Cumulation : Volumes 1-10, March 1964--February 1974

Author: Richard K. Gardner,Phyllis Grumm

Publisher: N.A


Category: Best books

Page: N.A

View: 4140

Time‒Frequency and Time‒Scale Methods

Adaptive Decompositions, Uncertainty Principles, and Sampling

Author: Jeffrey A. Hogan

Publisher: Springer Science & Business Media

ISBN: 9780817644314

Category: Mathematics

Page: 390

View: 5960

Developed in this book are several deep connections between time-frequency (Fourier/Gabor) analysis and time-scale (wavelet) analysis, emphasizing the powerful adaptive methods that emerge when separate techniques from each area are properly assembled in a larger context. While researchers at the forefront of these areas are well aware of the benefits of such a unified approach, there remains a knowledge gap in the larger community of practitioners about the precise strengths and limitations of Fourier/Gabor analysis versus wavelets. This book fills that gap by presenting the interface of time-frequency and time-scale methods as a rich area of work. "Foundations of Time-Frequency and Time-Scale Methods" will be suitable for applied mathematicians and engineers in signal/image processing and communication theory, as well as researchers and students in mathematical analysis, signal analysis, and mathematical physics.

Reihe B--Angewandte Geodäsie

Author: Institut für Angewandte Geodäsie (Deutsches Geodätisches Forschungsinstitut),Wolfgang Torge

Publisher: N.A


Category: Geodesy

Page: N.A

View: 6217