Frames And Other Bases In Abstract And Function Spaces
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Frames And Other Bases In Abstract And Function Spaces
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Author : Isaac Pesenson
language : en
Publisher: Birkhäuser
Release Date : 2017-06-11
Frames And Other Bases In Abstract And Function Spaces written by Isaac Pesenson and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-11 with Mathematics categories.
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.
Excursions In Harmonic Analysis Volume 6
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Author : Matthew Hirn
language : en
Publisher: Springer Nature
Release Date : 2021-09-01
Excursions In Harmonic Analysis Volume 6 written by Matthew Hirn and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-01 with Mathematics categories.
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.
Analysis Approximation Optimization Computation And Applications
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Author : Marija P. Stanić
language : en
Publisher: Springer Nature
Release Date : 2025-07-14
Analysis Approximation Optimization Computation And Applications written by Marija P. Stanić and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-14 with Mathematics categories.
This contributed volume is dedicated to Academician Gradimir V. Milovanović on his 75th birthday and contains recent results in the fields of approximation theory, numerical analysis, mathematical analysis, optimization theory, and various applications of an interdisciplinary character. Most of these results were presented in person during an International Conference “Analysis, Approximations and Applications" (AAA2023), organized by the Faculty of Science, University of Kragujevac in Vrnjačka Banja, Serbia (June 21-24, 2023). This book is intended for researchers and students of mathematics and other computational and applied sciences. This book provides surveys of state of the art results in the fields of Extremal Problems, Optimization and Calculus of Variations; Orthogonal Systems and Quadrature Formulas; Differential and Integral Equations, Integral Transforms and Operation Calculus; Analytic Number Theory and Special Functions; Real and Complex Functions, Sequences, Series, Approximations and Expansions; Functional Analysis, Operator Theory, Fixed Point Theory and Iterative Processes, as well as in Miscellaneous Applications.
Sampling Theory And Applications
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Author : Stephen D. Casey
language : en
Publisher: Springer Nature
Release Date : 2020-05-20
Sampling Theory And Applications written by Stephen D. Casey and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-20 with Mathematics categories.
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.
Framelets And Wavelets
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Author : Bin Han
language : en
Publisher: Springer
Release Date : 2018-01-04
Framelets And Wavelets written by Bin Han and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-04 with Mathematics categories.
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.
Harmonic Analysis And Partial Differential Equations
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Author : Justin Feuto
language : en
Publisher: Springer Nature
Release Date : 2024-09-12
Harmonic Analysis And Partial Differential Equations written by Justin Feuto and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-12 with Mathematics categories.
This proceedings volume collects selected papers presented at the Harmonic Analysis and Applications Workshop held in Abidjan, Côte d'Ivoire from May 22-26, 2023. Chapters present surveys and recent research results from experts and cover a range of topics at the intersections of classical and abstract harmonic analysis, PDEs, and numerical analysis.
Adventures In Graph Theory
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Author : W. David Joyner
language : en
Publisher: Birkhäuser
Release Date : 2017-12-28
Adventures In Graph Theory written by W. David Joyner and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-28 with Mathematics categories.
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.
The Xft Quadrature In Discrete Fourier Analysis
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Author : Rafael G. Campos
language : en
Publisher: Springer
Release Date : 2019-05-24
The Xft Quadrature In Discrete Fourier Analysis written by Rafael G. Campos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-24 with Mathematics categories.
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.
Modulation Spaces
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Author : Árpád Bényi
language : en
Publisher: Springer Nature
Release Date : 2020-02-22
Modulation Spaces written by Árpád Bényi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-22 with Mathematics categories.
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.
Harmonic Analysis
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Author : Palle E.T. Jorgensen
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-10-30
Harmonic Analysis written by Palle E.T. Jorgensen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-30 with Mathematics categories.
There is a recent and increasing interest in harmonic analysis of non-smooth geometries. Real-world examples where these types of geometry appear include large computer networks, relationships in datasets, and fractal structures such as those found in crystalline substances, light scattering, and other natural phenomena where dynamical systems are present. Notions of harmonic analysis focus on transforms and expansions and involve dual variables. In this book on smooth and non-smooth harmonic analysis, the notion of dual variables will be adapted to fractals. In addition to harmonic analysis via Fourier duality, the author also covers multiresolution wavelet approaches as well as a third tool, namely, L2 spaces derived from appropriate Gaussian processes. The book is based on a series of ten lectures delivered in June 2018 at a CBMS conference held at Iowa State University.