Frames And Other Bases In Abstract And Function Spaces

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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 : 55,5 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.

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 : 41,9 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 : 46,9 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.

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 : 49,6 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.

Scale Space and Variational Methods in Computer Vision

Abderrahim Elmoataz,Jalal Fadili,Yvain Quéau,Julien Rabin,Loïc Simon
Scale Space and Variational Methods in Computer Vision Book PDF

Author : Abderrahim Elmoataz,Jalal Fadili,Yvain Quéau,Julien Rabin,Loïc Simon
Publisher : Springer Nature
Page : 584 pages
File Size : 46,7 Mb
Release : 2021-04-29
Category : Computers
ISBN : 9783030755492

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Scale Space and Variational Methods in Computer Vision by Abderrahim Elmoataz,Jalal Fadili,Yvain Quéau,Julien Rabin,Loïc Simon Pdf

This book constitutes the proceedings of the 8th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2021, which took place during May 16-20, 2021. The conference was planned to take place in Cabourg, France, but changed to an online format due to the COVID-19 pandemic. The 45 papers included in this volume were carefully reviewed and selected from a total of 64 submissions. They were organized in topical sections named as follows: scale space and partial differential equations methods; flow, motion and registration; optimization theory and methods in imaging; machine learning in imaging; segmentation and labelling; restoration, reconstruction and interpolation; and inverse problems in imaging.

Adventures in Graph Theory

W. David Joyner,Caroline Grant Melles
Adventures in Graph Theory Book PDF

Author : W. David Joyner,Caroline Grant Melles
Publisher : Birkhäuser
Page : 327 pages
File Size : 47,9 Mb
Release : 2017-12-28
Category : Mathematics
ISBN : 9783319683836

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Adventures in Graph Theory by W. David Joyner,Caroline Grant Melles Pdf

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. An overview of graph theory definitions and polynomial invariants for graphs prepares the reader for the subsequent dive into the applications of graph theory. To pique the reader’s interest in areas of possible exploration, recent results in mathematics appear throughout the book, accompanied with examples of related graphs, how they arise, and what their valuable uses are. The consequences of graph theory covered by the authors are complicated and far-reaching, so topics are always exhibited in a user-friendly manner with copious graphs, exercises, and Sage code for the computation of equations. Samples of the book’s source code can be found at github.com/springer-math/adventures-in-graph-theory. The text is geared towards advanced undergraduate and graduate students and is particularly useful for those trying to decide what type of problem to tackle for their dissertation. This book can also serve as a reference for anyone interested in exploring how they can apply graph theory to other parts of mathematics.

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 Nature
Page : 676 pages
File Size : 44,8 Mb
Release : 2023-11-08
Category : Mathematics
ISBN : 9783031350054

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

New technological innovations and advances in research in areas such as spectroscopy, computer tomography, signal processing, and data analysis require a deep understanding of function approximation using Fourier methods. To address this growing need, this monograph combines mathematical theory and numerical algorithms to offer a unified and self-contained presentation of Fourier analysis. The first four chapters of the text serve as an introduction to classical Fourier analysis in the univariate and multivariate cases, including the discrete Fourier transforms, providing the necessary background for all further chapters. Next, chapters explore the construction and analysis of corresponding fast algorithms in the one- and multidimensional cases. The well-known fast Fourier transforms (FFTs) are discussed, as well as recent results on the construction of the nonequispaced FFTs, high-dimensional FFTs on special lattices, and sparse FFTs. An additional chapter is devoted to discrete trigonometric transforms and Chebyshev expansions. The final two chapters consider various applications of numerical Fourier methods for improved function approximation, including Prony methods for the recovery of structured functions. This new edition has been revised and updated throughout, featuring new material on a new Fourier approach to the ANOVA decomposition of high-dimensional trigonometric polynomials; new research results on the approximation errors of the nonequispaced fast Fourier transform based on special window functions; and the recently developed ESPIRA algorithm for recovery of exponential sums, among others. Numerical Fourier Analysis will be of interest to graduate students and researchers in applied mathematics, physics, computer science, engineering, and other areas where Fourier methods play an important role in applications.

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 : 50,7 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.

Framelets and Wavelets

Bin Han
Framelets and Wavelets Book PDF

Author : Bin Han
Publisher : Springer
Page : 750 pages
File Size : 55,8 Mb
Release : 2018-01-04
Category : Mathematics
ISBN : 9783319685304

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Framelets and Wavelets by Bin Han Pdf

Marking a distinct departure from the perspectives of frame theory and discrete transforms, this book provides a comprehensive mathematical and algorithmic introduction to wavelet theory. As such, it can be used as either a textbook or reference guide. As a textbook for graduate mathematics students and beginning researchers, it offers detailed information on the basic theory of framelets and wavelets, complemented by self-contained elementary proofs, illustrative examples/figures, and supplementary exercises. Further, as an advanced reference guide for experienced researchers and practitioners in mathematics, physics, and engineering, the book addresses in detail a wide range of basic and advanced topics (such as multiwavelets/multiframelets in Sobolev spaces and directional framelets) in wavelet theory, together with systematic mathematical analysis, concrete algorithms, and recent developments in and applications of framelets and wavelets. Lastly, the book can also be used to teach on or study selected special topics in approximation theory, Fourier analysis, applied harmonic analysis, functional analysis, and wavelet-based signal/image processing.

Metrics, Norms, Inner Products, and Operator Theory

Christopher Heil
Metrics Norms Inner Products and Operator Theory Book PDF

Author : Christopher Heil
Publisher : Birkhäuser
Page : 359 pages
File Size : 47,8 Mb
Release : 2018-08-28
Category : Mathematics
ISBN : 9783319653228

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Metrics, Norms, Inner Products, and Operator Theory by Christopher Heil Pdf

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. With an emphasis on the fundamental properties defining the spaces, this book guides readers to a deeper understanding of analysis and an appreciation of the field as the “science of functions.” Many important topics that are rarely presented in an accessible way to undergraduate students are included, such as unconditional convergence of series, Schauder bases for Banach spaces, the dual of lp topological isomorphisms, the Spectral Theorem, the Baire Category Theorem, and the Uniform Boundedness Principle. The text is constructed in such a way that instructors have the option whether to include more advanced topics. Written in an appealing and accessible style, Metrics, Norms, Inner Products, and Operator Theory is suitable for independent study or as the basis for an undergraduate-level course. Instructors have several options for building a course around the text depending on the level and interests of their students. Key features: Aimed at students who have a basic knowledge of undergraduate real analysis. All of the required background material is reviewed in the first chapter. Suitable for undergraduate-level courses; no familiarity with measure theory is required. Extensive exercises complement the text and provide opportunities for learning by doing. A separate solutions manual is available for instructors via the Birkhäuser website (www.springer.com/978-3-319-65321-1). Unique text providing an undergraduate-level introduction to metrics, norms, inner products, and their associated operator theory.

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 : 55,9 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 : 42,6 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 : 43,7 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.

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 : 45,7 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.

Topics in Classical and Modern Analysis

Martha Abell,Emil Iacob,Alex Stokolos,Sharon Taylor,Sergey Tikhonov,Jiehua Zhu
Topics in Classical and Modern Analysis Book PDF

Author : Martha Abell,Emil Iacob,Alex Stokolos,Sharon Taylor,Sergey Tikhonov,Jiehua Zhu
Publisher : Springer Nature
Page : 373 pages
File Size : 53,5 Mb
Release : 2019-10-21
Category : Mathematics
ISBN : 9783030122775

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Topics in Classical and Modern Analysis by Martha Abell,Emil Iacob,Alex Stokolos,Sharon Taylor,Sergey Tikhonov,Jiehua Zhu Pdf

Different aspects of harmonic analysis, complex analysis, sampling theory, approximation theory and related topics are covered in this volume. The topics included are Fourier analysis, Padè approximation, dynamical systems and difference operators, splines, Christoffel functions, best approximation, discrepancy theory and Jackson-type theorems of approximation. The articles of this collection were originated from the International Conference in Approximation Theory, held in Savannah, GA in 2017, and organized by the editors of this volume.