Recent Applications Of Harmonic Analysis To Function Spaces Differential Equations And Data Science

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

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

Author : Isaac Pesenson,Quoc Thong Le Gia,Azita Mayeli,Hrushikesh Mhaskar,Ding-Xuan Zhou
Publisher : Birkhäuser
Page : 510 pages
File Size : 40,5 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.

Modulation Spaces

Árpád Bényi,Kasso A. Okoudjou
Modulation Spaces Book PDF

Author : Árpád Bényi,Kasso A. Okoudjou
Publisher : Springer Nature
Page : 177 pages
File Size : 55,5 Mb
Release : 2020-02-22
Category : Mathematics
ISBN : 9781071603321

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Modulation Spaces by Árpád Bényi,Kasso A. Okoudjou Pdf

This monograph serves as a much-needed, self-contained reference on the topic of modulation spaces. By gathering together state-of-the-art developments and previously unexplored applications, readers will be motivated to make effective use of this topic in future research. Because modulation spaces have historically only received a cursory treatment, this book will fill a gap in time-frequency analysis literature, and offer readers a convenient and timely resource. Foundational concepts and definitions in functional, harmonic, and real analysis are reviewed in the first chapter, which is then followed by introducing modulation spaces. The focus then expands to the many valuable applications of modulation spaces, such as linear and multilinear pseudodifferential operators, and dispersive partial differential equations. Because it is almost entirely self-contained, these insights will be accessible to a wide audience of interested readers. Modulation Spaces will be an ideal reference for researchers in time-frequency analysis and nonlinear partial differential equations. It will also appeal to graduate students and seasoned researchers who seek an introduction to the time-frequency analysis of nonlinear dispersive partial differential equations.

Frames and Other Bases in Abstract and Function Spaces

Isaac Pesenson,Quoc Thong Le Gia,Azita Mayeli,Hrushikesh Mhaskar,Ding-Xuan Zhou
Frames and Other Bases in Abstract and Function Spaces Book PDF

Author : Isaac Pesenson,Quoc Thong Le Gia,Azita Mayeli,Hrushikesh Mhaskar,Ding-Xuan Zhou
Publisher : Birkhäuser
Page : 438 pages
File Size : 44,9 Mb
Release : 2017-06-11
Category : Mathematics
ISBN : 9783319555508

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Frames and Other Bases in Abstract and Function Spaces by Isaac Pesenson,Quoc Thong Le Gia,Azita Mayeli,Hrushikesh Mhaskar,Ding-Xuan Zhou Pdf

The first 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 I is organized around the theme of frames and other bases in abstract and function spaces, covering topics such as: The advanced development of frames, including Sigma-Delta quantization for fusion frames, localization of frames, and frame conditioning, as well as applications to distributed sensor networks, Galerkin-like representation of operators, scaling on graphs, and dynamical sampling. A systematic approach to shearlets with applications to wavefront sets and function spaces. Prolate and generalized prolate functions, spherical Gauss-Laguerre basis functions, and radial basis functions. Kernel methods, wavelets, and frames on compact and non-compact manifolds.

Numerical Fourier Analysis

Gerlind Plonka,Daniel Potts,Gabriele Steidl,Manfred Tasche
Numerical Fourier Analysis Book PDF

Author : Gerlind Plonka,Daniel Potts,Gabriele Steidl,Manfred Tasche
Publisher : Springer
Page : 618 pages
File Size : 42,6 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.

Convergence and Summability of Fourier Transforms and Hardy Spaces

Ferenc Weisz
Convergence and Summability of Fourier Transforms and Hardy Spaces Book PDF

Author : Ferenc Weisz
Publisher : Birkhäuser
Page : 435 pages
File Size : 53,7 Mb
Release : 2017-12-27
Category : Mathematics
ISBN : 9783319568140

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Convergence and Summability of Fourier Transforms and Hardy Spaces by Ferenc Weisz Pdf

This book investigates the convergence and summability of both one-dimensional and multi-dimensional Fourier transforms, as well as the theory of Hardy spaces. To do so, it studies a general summability method known as theta-summation, which encompasses all the well-known summability methods, such as the Fejér, Riesz, Weierstrass, Abel, Picard, Bessel and Rogosinski summations. Following on the classic books by Bary (1964) and Zygmund (1968), this is the first book that considers strong summability introduced by current methodology. A further unique aspect is that the Lebesgue points are also studied in the theory of multi-dimensional summability. In addition to classical results, results from the past 20-30 years – normally only found in scattered research papers – are also gathered and discussed, offering readers a convenient “one-stop” source to support their work. As such, the book will be useful for researchers, graduate and postgraduate students alike.

Recent Advances in Harmonic Analysis and Applications

Dmitriy Bilyk,Laura De Carli,Alexander Petukhov,Alexander M. Stokolos,Brett D. Wick
Recent Advances in Harmonic Analysis and Applications Book PDF

Author : Dmitriy Bilyk,Laura De Carli,Alexander Petukhov,Alexander M. Stokolos,Brett D. Wick
Publisher : Springer Science & Business Media
Page : 408 pages
File Size : 51,7 Mb
Release : 2012-10-16
Category : Mathematics
ISBN : 9781461445654

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Recent Advances in Harmonic Analysis and Applications by Dmitriy Bilyk,Laura De Carli,Alexander Petukhov,Alexander M. Stokolos,Brett D. Wick Pdf

Recent Advances in Harmonic Analysis and Applications features selected contributions from the AMS conference which took place at Georgia Southern University, Statesboro in 2011 in honor of Professor Konstantin Oskolkov's 65th birthday. The contributions are based on two special sessions, namely "Harmonic Analysis and Applications" and "Sparse Data Representations and Applications." Topics covered range from Banach space geometry to classical harmonic analysis and partial differential equations. Survey and expository articles by leading experts in their corresponding fields are included, and the volume also features selected high quality papers exploring new results and trends in Muckenhoupt-Sawyer theory, orthogonal polynomials, trigonometric series, approximation theory, Bellman functions and applications in differential equations. Graduate students and researchers in analysis will be particularly interested in the articles which emphasize remarkable connections between analysis and analytic number theory. The readers will learn about recent mathematical developments and directions for future work in the unexpected and surprising interaction between abstract problems in additive number theory and experimentally discovered optical phenomena in physics. This book will be useful for number theorists, harmonic analysts, algorithmists in multi-dimensional signal processing and experts in physics and partial differential equations.

Compressed Sensing and Its Applications

Holger Boche,Giuseppe Caire,Robert Calderbank,Gitta Kutyniok,Rudolf Mathar,Philipp Petersen
Compressed Sensing and Its Applications Book PDF

Author : Holger Boche,Giuseppe Caire,Robert Calderbank,Gitta Kutyniok,Rudolf Mathar,Philipp Petersen
Publisher : Birkhäuser
Page : 305 pages
File Size : 49,6 Mb
Release : 2019-08-13
Category : Mathematics
ISBN : 9783319730745

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Compressed Sensing and Its Applications by Holger Boche,Giuseppe Caire,Robert Calderbank,Gitta Kutyniok,Rudolf Mathar,Philipp Petersen Pdf

The chapters in this volume highlight the state-of-the-art of compressed sensing and are based on talks given at the third international MATHEON conference on the same topic, held from December 4-8, 2017 at the Technical University in Berlin. In addition to methods in compressed sensing, chapters provide insights into cutting edge applications of deep learning in data science, highlighting the overlapping ideas and methods that connect the fields of compressed sensing and deep learning. Specific topics covered include: Quantized compressed sensing Classification Machine learning Oracle inequalities Non-convex optimization Image reconstruction Statistical learning theory This volume will be a valuable resource for graduate students and researchers in the areas of mathematics, computer science, and engineering, as well as other applied scientists exploring potential applications of compressed sensing.

Sampling: Theory and Applications

Stephen D. Casey,Kasso A. Okoudjou,Michael Robinson,Brian M. Sadler
Sampling Theory and Applications Book PDF

Author : Stephen D. Casey,Kasso A. Okoudjou,Michael Robinson,Brian M. Sadler
Publisher : Springer Nature
Page : 210 pages
File Size : 41,9 Mb
Release : 2020-05-20
Category : Mathematics
ISBN : 9783030362911

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Sampling: Theory and Applications by Stephen D. Casey,Kasso A. Okoudjou,Michael Robinson,Brian M. Sadler Pdf

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 issues Sampling: Theory and Applications is ideal for mathematicians, engineers, and applied scientists working in sampling theory or related areas.

Excursions in Harmonic Analysis, Volume 6

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

Author : Matthew Hirn,Shidong Li,Kasso A. Okoudjou,Sandra Saliani,Özgür Yilmaz
Publisher : Springer Nature
Page : 444 pages
File Size : 40,6 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.

Harmonic and Applied Analysis

Filippo De Mari,Ernesto De Vito
Harmonic and Applied Analysis Book PDF

Author : Filippo De Mari,Ernesto De Vito
Publisher : Springer Nature
Page : 316 pages
File Size : 52,9 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.

The XFT Quadrature in Discrete Fourier Analysis

Rafael G. Campos
The XFT Quadrature in Discrete Fourier Analysis Book PDF

Author : Rafael G. Campos
Publisher : Springer
Page : 235 pages
File Size : 42,8 Mb
Release : 2019-05-24
Category : Mathematics
ISBN : 9783030134235

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The XFT Quadrature in Discrete Fourier Analysis by Rafael G. Campos Pdf

This book has two main objectives, the first of which is to extend the power of numerical Fourier analysis and to show by means of theoretical examples and numerous concrete applications that when computing discrete Fourier transforms of periodic and non periodic functions, the usual kernel matrix of the Fourier transform, the discrete Fourier transform (DFT), should be replaced by another kernel matrix, the eXtended Fourier transform (XFT), since the XFT matrix appears as a convergent quadrature of a more general transform, the fractional Fourier transform. In turn, the book’s second goal is to present the XFT matrix as a finite-dimensional transformation that links certain discrete operators in the same way that the corresponding continuous operators are related by the Fourier transform, and to show that the XFT matrix accordingly generates sequences of matrix operators that represent continuum operators, and which allow these operators to be studied from another perspective.

Advances in Microlocal and Time-Frequency Analysis

Paolo Boggiatto,Marco Cappiello,Elena Cordero,Sandro Coriasco,Gianluca Garello,Alessandro Oliaro,Jörg Seiler
Advances in Microlocal and Time Frequency Analysis Book PDF

Author : Paolo Boggiatto,Marco Cappiello,Elena Cordero,Sandro Coriasco,Gianluca Garello,Alessandro Oliaro,Jörg Seiler
Publisher : Springer Nature
Page : 533 pages
File Size : 55,8 Mb
Release : 2020-03-03
Category : Mathematics
ISBN : 9783030361389

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Advances in Microlocal and Time-Frequency Analysis by Paolo Boggiatto,Marco Cappiello,Elena Cordero,Sandro Coriasco,Gianluca Garello,Alessandro Oliaro,Jörg Seiler Pdf

The present volume gathers contributions to the conference Microlocal and Time-Frequency Analysis 2018 (MLTFA18), which was held at Torino University from the 2nd to the 6th of July 2018. The event was organized in honor of Professor Luigi Rodino on the occasion of his 70th birthday. The conference’s focus and the contents of the papers reflect Luigi’s various research interests in the course of his long and extremely prolific career at Torino University.

Sampling, Approximation, and Signal Analysis

Stephen D. Casey,M. Maurice Dodson,Paulo J. S. G. Ferreira,Ahmed Zayed
Sampling Approximation and Signal Analysis Book PDF

Author : Stephen D. Casey,M. Maurice Dodson,Paulo J. S. G. Ferreira,Ahmed Zayed
Publisher : Springer Nature
Page : 580 pages
File Size : 48,9 Mb
Release : 2024-01-04
Category : Mathematics
ISBN : 9783031411304

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Sampling, Approximation, and Signal Analysis by Stephen D. Casey,M. Maurice Dodson,Paulo J. S. G. Ferreira,Ahmed Zayed Pdf

During his long and distinguished career, J. Rowland Higgins (1935-2020) made a substantial impact on many mathematical fields through his work on sampling theory, his deep knowledge of its history, and his service to the community. This volume is a tribute to his work and legacy, featuring chapters written by distinguished mathematicians that explore cutting-edge research in sampling, approximation, signal analysis, and other related areas. An introductory chapter provides a biography of Higgins that explores his rich and unique life, along with a bibliography of his papers; a brief history of the SampTA meetings – of which he was a Founding Member – is also included. The remaining articles are grouped into four sections – classical sampling, theoretical extensions, frame theory, and applications of sampling theory – and explore Higgins’ contributions to these areas, as well as some of the latest developments.

From Classical Analysis to Analysis on Fractals

Patricia Alonso Ruiz,Michael Hinz,Kasso A. Okoudjou,Luke G. Rogers,Alexander Teplyaev
From Classical Analysis to Analysis on Fractals Book PDF

Author : Patricia Alonso Ruiz,Michael Hinz,Kasso A. Okoudjou,Luke G. Rogers,Alexander Teplyaev
Publisher : Springer Nature
Page : 294 pages
File Size : 48,8 Mb
Release : 2023-11-25
Category : Mathematics
ISBN : 9783031378003

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From Classical Analysis to Analysis on Fractals by Patricia Alonso Ruiz,Michael Hinz,Kasso A. Okoudjou,Luke G. Rogers,Alexander Teplyaev Pdf

Over the course of his distinguished career, Robert Strichartz (1943-2021) had a substantial impact on the field of analysis with his deep, original results in classical harmonic, functional, and spectral analysis, and in the newly developed analysis on fractals. This is the first volume of a tribute to his work and legacy, featuring chapters that reflect his mathematical interests, written by his colleagues and friends. An introductory chapter summarizes his broad and varied mathematical work and highlights his profound contributions as a mathematical mentor. The remaining articles are grouped into three sections – functional and harmonic analysis on Euclidean spaces, analysis on manifolds, and analysis on fractals – and explore Strichartz’ contributions to these areas, as well as some of the latest developments.

Theoretical Physics, Wavelets, Analysis, Genomics

Patrick Flandrin,Stéphane Jaffard,Thierry Paul,Bruno Torresani
Theoretical Physics Wavelets Analysis Genomics Book PDF

Author : Patrick Flandrin,Stéphane Jaffard,Thierry Paul,Bruno Torresani
Publisher : Springer Nature
Page : 650 pages
File Size : 40,9 Mb
Release : 2023-05-31
Category : Mathematics
ISBN : 9783030458478

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Theoretical Physics, Wavelets, Analysis, Genomics by Patrick Flandrin,Stéphane Jaffard,Thierry Paul,Bruno Torresani Pdf

Over the course of a scientific career spanning more than fifty years, Alex Grossmann (1930-2019) made many important contributions to a wide range of areas including, among others, mathematics, numerical analysis, physics, genetics, and biology. His lasting influence can be seen not only in his research and numerous publications, but also through the relationships he cultivated with his collaborators and students. This edited volume features chapters written by some of these colleagues, as well as researchers whom Grossmann’s work and way of thinking has impacted in a decisive way. Reflecting the diversity of his interests and their interdisciplinary nature, these chapters explore a variety of current topics in quantum mechanics, elementary particles, and theoretical physics; wavelets and mathematical analysis; and genomics and biology. A scientific biography of Grossmann, along with a more personal biography written by his son, serve as an introduction. Also included are the introduction to his PhD thesis and an unpublished paper coauthored by him. Researchers working in any of the fields listed above will find this volume to be an insightful and informative work.