Explorations In Harmonic Analysis
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Explorations In Harmonic Analysis
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Author : Steven G. Krantz
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-24
Explorations In Harmonic Analysis written by Steven G. Krantz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-24 with Mathematics categories.
This self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis.
Explorations In Complex Analysis
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Author : Michael A. Brilleslyper
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-12-31
Explorations In Complex Analysis written by Michael A. Brilleslyper 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 2012-12-31 with Mathematics categories.
Research topics in the book include complex dynamics, minimal surfaces, fluid flows, harmonic, conformal, and polygonal mappings, and discrete complex analysis via circle packing. The nature of this book is different from many mathematics texts: the focus is on student-driven and technology-enhanced investigation. Interlaced in the reading for each chapter are examples, exercises, explorations, and projects, nearly all linked explicitly with computer applets for visualization and hands-on manipulation.
On The Shoulders Of Giants An Exploration Of Complex Analysis
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-07-20
On The Shoulders Of Giants An Exploration Of Complex Analysis written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-20 with Science categories.
Embark on an intellectual journey through the captivating world of complex analysis, where numbers transcend the boundaries of reality and unveil hidden symmetries of the mathematical universe. This book is an invitation to explore the realm of complex numbers, extending beyond the familiar confines of real numbers to unlock a treasure trove of insights and applications. Within these pages, you will unravel the mysteries of complex functions, delving into their unique properties and behaviors. Discover the intricacies of integration in the complex plane, a powerful tool for solving intricate problems that defy traditional methods. As you progress through the chapters, you will encounter a symphony of fascinating topics, from power series and Laurent expansions to conformal mappings and analytic functions. Each concept is meticulously explained with clarity and precision, ensuring that readers can grasp the underlying principles and appreciate their profound significance. Furthermore, this book illuminates the diverse applications of complex analysis across various disciplines, showcasing its versatility and impact. From electrical engineering and fluid mechanics to quantum mechanics and image processing, complex analysis has revolutionized the scientific landscape. This book is meticulously crafted for students, researchers, and practitioners seeking a comprehensive understanding of complex analysis. Its clear and engaging writing style, coupled with numerous illustrative examples and exercises, makes it an invaluable resource for anyone eager to delve into this captivating field. Join us on this intellectual odyssey as we traverse the intricate landscapes of complex analysis, uncovering hidden truths and unlocking the power of this mathematical realm. Let us witness the transformative impact of complex analysis on diverse fields of knowledge and experience the profound beauty of this mathematical tapestry. If you like this book, write a review!
Excursions In Harmonic Analysis Volume 3
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Author : Radu Balan
language : en
Publisher: Birkhäuser
Release Date : 2015-06-02
Excursions In Harmonic Analysis Volume 3 written by Radu Balan and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-02 with Mathematics categories.
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.
Excursions In Harmonic Analysis Volume 4
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Author : Radu Balan
language : en
Publisher: Birkhäuser
Release Date : 2015-10-20
Excursions In Harmonic Analysis Volume 4 written by Radu Balan and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-20 with Mathematics categories.
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.
Real Variable Methods In Harmonic Analysis
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Author : Alberto Torchinsky
language : en
Publisher: Courier Corporation
Release Date : 2004-04-09
Real Variable Methods In Harmonic Analysis written by Alberto Torchinsky and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-04-09 with Mathematics categories.
An exploration of the unity of several areas in harmonic analysis, this text emphasizes real-variable methods. Discusses classical Fourier series, summability, norm convergence, and conjugate function. Examines the Hardy-Littlewood maximal function, the Calderón-Zygmund decomposition, the Hilbert transform and properties of harmonic functions, the Littlewood-Paley theory, more. 1986 edition.
The Evolution Of Applied Harmonic Analysis
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Author : Elena Prestini
language : en
Publisher: Birkhäuser
Release Date : 2016-12-01
The Evolution Of Applied Harmonic Analysis written by Elena Prestini and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-01 with Mathematics categories.
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
Excursions In Harmonic Analysis Volume 5
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Author : Radu Balan
language : en
Publisher: Birkhäuser
Release Date : 2017-06-20
Excursions In Harmonic Analysis Volume 5 written by Radu Balan and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-20 with Mathematics categories.
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.
Recent Applications Of Harmonic Analysis To Function Spaces Differential Equations And Data Science
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Author : Isaac Pesenson
language : en
Publisher: Birkhäuser
Release Date : 2017-08-09
Recent Applications Of Harmonic Analysis To Function Spaces Differential Equations And Data Science 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 2017-08-09 with Mathematics categories.
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.
New Trends In Applied Harmonic Analysis Volume 2
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Author : Akram Aldroubi
language : en
Publisher: Springer Nature
Release Date : 2019-11-26
New Trends In Applied Harmonic Analysis Volume 2 written by Akram Aldroubi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-26 with Mathematics categories.
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.