Four Short Courses On Harmonic Analysis

Author : Brigitte Forster,Peter Robert Massopust
Publisher : Springer Science & Business Media
Page : 265 pages
File Size : 43,6 Mb
Release : 2010
Category : Mathematics
ISBN : 9780817648909

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Four Short Courses on Harmonic Analysis by Brigitte Forster,Peter Robert Massopust Pdf

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.

Author : Brigitte Forster,Peter Massopust
Publisher : Unknown
Page : 268 pages
File Size : 42,5 Mb
Release : 2009-11-05
Category : Electronic
ISBN : 0817648941

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Four Short Courses on Harmonic Analysis by Brigitte Forster,Peter Massopust Pdf

Author : Radu Balan,Matthew Begué,John J. Benedetto,Wojciech Czaja,Kasso A. Okoudjou
Publisher : Birkhäuser
Page : 428 pages
File Size : 41,6 Mb
Release : 2015-10-20
Category : Mathematics
ISBN : 9783319201887

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Excursions in Harmonic Analysis, Volume 4 by Radu Balan,Matthew Begué,John J. Benedetto,Wojciech Czaja,Kasso A. Okoudjou Pdf

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. Containing cutting-edge results by an impressive array of mathematicians, engineers and scientists in academia, industry and government, it will be an excellent reference for graduate students, researchers and professionals in pure and applied mathematics, physics and engineering. Topics covered include: Special Topics in Harmonic Analysis Applications and Algorithms in the Physical Sciences Gabor Theory RADAR and Communications: Design, Theory, and Applications The February Fourier Talks are held annually at the Norbert Wiener Center for Harmonic Analysis and Applications. Located at the University of Maryland, College Park, the Norbert Wiener Center provides a state-of- the-art research venue for the broad emerging area of mathematical engineering.

Author : Radu Balan,Matthew J. Begué,John J. Benedetto,Wojciech Czaja,Kasso A. Okoudjou
Publisher : Birkhäuser
Page : 336 pages
File Size : 49,9 Mb
Release : 2015-06-02
Category : Mathematics
ISBN : 9783319132303

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Excursions in Harmonic Analysis, Volume 3 by Radu Balan,Matthew J. Begué,John J. Benedetto,Wojciech Czaja,Kasso A. Okoudjou Pdf

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. Containing cutting-edge results by an impressive array of mathematicians, engineers, and scientists in academia, industry, and government, it will be an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, physics, and engineering. Topics covered include · spectral analysis and correlation; · radar and communications: design, theory, and applications; · sparsity · special topics in harmonic analysis. The February Fourier Talks are held annually at the Norbert Wiener Center for Harmonic Analysis and Applications. Located at the University of Maryland, College Park, the Norbert Wiener Center provides a state-of- the-art research venue for the broad emerging area of mathematical engineering.

Author : Carlos Cabrelli,Jose Luis Torrea
Publisher : Springer Science & Business Media
Page : 215 pages
File Size : 45,7 Mb
Release : 2010-03-10
Category : Mathematics
ISBN : 9780817645885

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Recent Developments in Real and Harmonic Analysis by Carlos Cabrelli,Jose Luis Torrea Pdf

A collection of invited chapters dedicated to Carlos Segovia, this unified and self-contained volume examines recent developments in real and harmonic analysis. The work begins with a chronological description of Segovia’s mathematical life, highlighting his original ideas and their evolution. Also included are surveys dealing with Carlos’ favorite topics, and PDE works written by students and colleagues close to Segovia whose careers were in some way influenced by him. Contributors: H. Aimar, A. Bonami, O. Blasco, L.A. Caffarelli, S. Chanillo, J. Feuto, L. Forzani, C.E. Gutíerrez, E. Harboure, A.L. Karakhanyan, C.E. Kenig, R.A. Macías, J.J. Manfredi, F.J. Martín-Reyes, P. Ortega, R. Scotto, A. de la Torre, J.L. Torrea.

Author : Gerlind Plonka,Daniel Potts,Gabriele Steidl,Manfred Tasche
Publisher : Springer
Page : 618 pages
File Size : 40,6 Mb
Release : 2019-02-05
Category : Mathematics
ISBN : 9783030043063

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Numerical Fourier Analysis by Gerlind Plonka,Daniel Potts,Gabriele Steidl,Manfred Tasche Pdf

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.

Author : Matthew Hirn,Shidong Li,Kasso A. Okoudjou,Sandra Saliani,Özgür Yilmaz
Publisher : Springer Nature
Page : 444 pages
File Size : 49,7 Mb
Release : 2021-09-01
Category : Mathematics
ISBN : 9783030696375

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Excursions in Harmonic Analysis, Volume 6 by Matthew Hirn,Shidong Li,Kasso A. Okoudjou,Sandra Saliani,Özgür Yilmaz Pdf

John J. Benedetto has had a profound influence not only on the direction of harmonic analysis and its applications, but also on the entire community of people involved in the field. The chapters in this volume – compiled on the occasion of his 80th birthday – are written by leading researchers in the field and pay tribute to John’s many significant and lasting achievements. Covering a wide range of topics in harmonic analysis and related areas, these chapters are organized into four main parts: harmonic analysis, wavelets and frames, sampling and signal processing, and compressed sensing and optimization. An introductory chapter also provides a brief overview of John’s life and mathematical career. This volume will be an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, engineering, and physics.

Author : Akram Aldroubi,Carlos Cabrelli,Stephane Jaffard,Ursula Molter
Publisher : Birkhäuser
Page : 334 pages
File Size : 41,9 Mb
Release : 2016-04-21
Category : Mathematics
ISBN : 9783319278735

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New Trends in Applied Harmonic Analysis by Akram Aldroubi,Carlos Cabrelli,Stephane Jaffard,Ursula Molter Pdf

This volume is a selection of written notes corresponding to courses taught at the CIMPA School: "New Trends in Applied Harmonic Analysis: Sparse Representations, Compressed Sensing and Multifractal Analysis". New interactions between harmonic analysis and signal and image processing have seen striking development in the last 10 years, and several technological deadlocks have been solved through the resolution of deep theoretical problems in harmonic analysis. New Trends in Applied Harmonic Analysis focuses on two particularly active areas that are representative of such advances: multifractal analysis, and sparse representation and compressed sensing. The contributions are written by leaders in these areas, and cover both theoretical aspects and applications. This work should prove useful not only to PhD students and postdocs in mathematics and signal and image processing, but also to researchers working in related topics.

Author : Akram Aldroubi,Carlos Cabrelli,Stéphane Jaffard,Ursula Molter
Publisher : Springer Nature
Page : 335 pages
File Size : 55,6 Mb
Release : 2019-11-26
Category : Mathematics
ISBN : 9783030323530

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New Trends in Applied Harmonic Analysis, Volume 2 by Akram Aldroubi,Carlos Cabrelli,Stéphane Jaffard,Ursula Molter Pdf

This contributed volume collects papers based on courses and talks given at the 2017 CIMPA school Harmonic Analysis, Geometric Measure Theory and Applications, which took place at the University of Buenos Aires in August 2017. These articles highlight recent breakthroughs in both harmonic analysis and geometric measure theory, particularly focusing on their impact on image and signal processing. The wide range of expertise present in these articles will help readers contextualize how these breakthroughs have been instrumental in resolving deep theoretical problems. Some topics covered include: Gabor frames Falconer distance problem Hausdorff dimension Sparse inequalities Fractional Brownian motion Fourier analysis in geometric measure theory This volume is ideal for applied and pure mathematicians interested in the areas of image and signal processing. Electrical engineers and statisticians studying these fields will also find this to be a valuable resource.

Author : Elena Prestini
Publisher : Birkhäuser
Page : 356 pages
File Size : 50,7 Mb
Release : 2016-12-01
Category : Mathematics
ISBN : 9781489979896

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The Evolution of Applied Harmonic Analysis by Elena Prestini Pdf

A sweeping exploration of the development and far-reaching applications of harmonic analysis such as signal processing, digital music, Fourier optics, radio astronomy, crystallography, medical imaging, spectroscopy, and more. Featuring a wealth of illustrations, examples, and material not found in other harmonic analysis books, this unique monograph skillfully blends together historical narrative with scientific exposition to create a comprehensive yet accessible work. While only an understanding of calculus is required to appreciate it, there are more technical sections that will charm even specialists in harmonic analysis. From undergraduates to professional scientists, engineers, and mathematicians, there is something for everyone here. The second edition of The Evolution of Applied Harmonic Analysis contains a new chapter on atmospheric physics and climate change, making it more relevant for today’s audience. Praise for the first edition: "...can be thoroughly recommended to any reader who is curious about the physical world and the intellectual underpinnings that have lead to our expanding understanding of our physical environment and to our halting steps to control it. Everyone who uses instruments that are based on harmonic analysis will benefit from the clear verbal descriptions that are supplied." — R.N. Bracewell, Stanford University “The book under review is a unique and splendid telling of the triumphs of the fast Fourier transform. I can recommend it unconditionally... Elena Prestini... has taken one major mathematical idea, that of Fourier analysis, and chased down and described a half dozen varied areas in which Fourier analysis and the FFT are now in place. Her book is much to be applauded.” — Society for Industrial and Applied Mathematics “This is not simply a book about mathematics, or even the history of mathematics; it is a story about how the discipline has been applied (to borrow Fourier’s expression) to ‘the public good and the explanation of natural phenomena.’ ... This book constitutes a significant addition to the library of popular mathematical works, and a valuable resource for students of mathematics.” — Mathematical Association of America Reviews

Author : Radu Balan,John J. Benedetto,Wojciech Czaja,Matthew Dellatorre,Kasso A. Okoudjou
Publisher : Birkhäuser
Page : 338 pages
File Size : 50,5 Mb
Release : 2017-06-20
Category : Mathematics
ISBN : 9783319547114

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Excursions in Harmonic Analysis, Volume 5 by Radu Balan,John J. Benedetto,Wojciech Czaja,Matthew Dellatorre,Kasso A. Okoudjou Pdf

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 – 2016. Containing cutting-edge results by an impressive array of mathematicians, engineers, and scientists in academia, industry and government, it will be an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, physics, and engineering. Topics covered include: Theoretical harmonic analysis Image and signal processing Quantization Algorithms and representations The February Fourier Talks are held annually at the Norbert Wiener Center for Harmonic Analysis and Applications. Located at the University of Maryland, College Park, the Norbert Wiener Center provides a state-of- the-art research venue for the broad emerging area of mathematical engineering.

Author : Filippo De Mari,Ernesto De Vito
Publisher : Springer Nature
Page : 316 pages
File Size : 41,8 Mb
Release : 2021-12-13
Category : Mathematics
ISBN : 9783030866648

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Harmonic and Applied Analysis by Filippo De Mari,Ernesto De Vito Pdf

Deep connections exist between harmonic and applied analysis and the diverse yet connected topics of machine learning, data analysis, and imaging science. This volume explores these rapidly growing areas and features contributions presented at the second and third editions of the Summer Schools on Applied Harmonic Analysis, held at the University of Genova in 2017 and 2019. Each chapter offers an introduction to essential material and then demonstrates connections to more advanced research, with the aim of providing an accessible entrance for students and researchers. Topics covered include ill-posed problems; concentration inequalities; regularization and large-scale machine learning; unitarization of the radon transform on symmetric spaces; and proximal gradient methods for machine learning and imaging.

Author : Isaac Pesenson,Quoc Thong Le Gia,Azita Mayeli,Hrushikesh Mhaskar,Ding-Xuan Zhou
Publisher : Birkhäuser
Page : 510 pages
File Size : 54,5 Mb
Release : 2017-08-09
Category : Mathematics
ISBN : 9783319555560

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Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science by Isaac Pesenson,Quoc Thong Le Gia,Azita Mayeli,Hrushikesh Mhaskar,Ding-Xuan Zhou Pdf

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.

Author : Stephan Dahlke,Filippo De Mari,Philipp Grohs,Demetrio Labate
Publisher : Birkhäuser
Page : 256 pages
File Size : 40,6 Mb
Release : 2015-09-12
Category : Mathematics
ISBN : 9783319188638

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Harmonic and Applied Analysis by Stephan Dahlke,Filippo De Mari,Philipp Grohs,Demetrio Labate Pdf

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.​

Author : Alexander Paprotny,Michael Thess
Publisher : Springer Science & Business Media
Page : 313 pages
File Size : 53,9 Mb
Release : 2013-12-03
Category : Computers
ISBN : 9783319013213

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Realtime Data Mining by Alexander Paprotny,Michael Thess Pdf

​​​​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. Furthermore, it presents promising results of numerous experiments on real-world data.​ The area of realtime data mining is currently developing at an exceptionally dynamic pace, and realtime data mining systems are the counterpart of today's “classic” data mining systems. Whereas the latter learn from historical data and then use it to deduce necessary actions, realtime analytics systems learn and act continuously and autonomously. In the vanguard of these new analytics systems are recommendation engines. They are principally found on the Internet, where all information is available in realtime and an immediate feedback is guaranteed. This monograph appeals to computer scientists and specialists in machine learning, especially from the area of recommender systems, because it conveys a new way of realtime thinking by considering recommendation tasks as control-theoretic problems. Realtime Data Mining: Self-Learning Techniques for Recommendation Engines will also interest application-oriented mathematicians because it consistently combines some of the most promising mathematical areas, namely control theory, multilevel approximation, and tensor factorization.