Explorations In Harmonic Analysis PDF Download
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Author | : Steven G. Krantz |
Publisher | : Springer Science & Business Media |
Total Pages | : 367 |
Release | : 2009-05-24 |
Genre | : Mathematics |
ISBN | : 0817646698 |
Download Explorations in Harmonic Analysis Book in PDF, ePub and Kindle
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.
Author | : Alberto Torchinsky |
Publisher | : Elsevier |
Total Pages | : 475 |
Release | : 2016-06-03 |
Genre | : Mathematics |
ISBN | : 1483268888 |
Download Real-Variable Methods in Harmonic Analysis Book in PDF, ePub and Kindle
Real-Variable Methods in Harmonic Analysis deals with the unity of several areas in harmonic analysis, with emphasis on real-variable methods. Active areas of research in this field are discussed, from the Calderón-Zygmund theory of singular integral operators to the Muckenhoupt theory of Ap weights and the Burkholder-Gundy theory of good ? inequalities. The Calderón theory of commutators is also considered. Comprised of 17 chapters, this volume begins with an introduction to the pointwise convergence of Fourier series of functions, followed by an analysis of Cesàro summability. The discussion then turns to norm convergence; the basic working principles of harmonic analysis, centered around the Calderón-Zygmund decomposition of locally integrable functions; and fractional integration. Subsequent chapters deal with harmonic and subharmonic functions; oscillation of functions; the Muckenhoupt theory of Ap weights; and elliptic equations in divergence form. The book also explores the essentials of the Calderón-Zygmund theory of singular integral operators; the good ? inequalities of Burkholder-Gundy; the Fefferman-Stein theory of Hardy spaces of several real variables; Carleson measures; and Cauchy integrals on Lipschitz curves. The final chapter presents the solution to the Dirichlet and Neumann problems on C1-domains by means of the layer potential methods. This monograph is intended for graduate students with varied backgrounds and interests, ranging from operator theory to partial differential equations.
Author | : Michael A. Brilleslyper |
Publisher | : American Mathematical Soc. |
Total Pages | : 373 |
Release | : 2012-12-31 |
Genre | : Mathematics |
ISBN | : 1614441081 |
Download Explorations in Complex Analysis Book in PDF, ePub and Kindle
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.
Author | : Elena Prestini |
Publisher | : Birkhäuser |
Total Pages | : 356 |
Release | : 2016-12-01 |
Genre | : Mathematics |
ISBN | : 1489979891 |
Download The Evolution of Applied Harmonic Analysis Book in PDF, ePub and Kindle
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 | : Steven George Krantz |
Publisher | : American Mathematical Soc. |
Total Pages | : 586 |
Release | : 2001 |
Genre | : Functions of several complex variables |
ISBN | : 0821827243 |
Download Function Theory of Several Complex Variables Book in PDF, ePub and Kindle
Emphasizing integral formulas, the geometric theory of pseudoconvexity, estimates, partial differential equations, approximation theory, inner functions, invariant metrics, and mapping theory, this title is intended for the student with a background in real and complex variable theory, harmonic analysis, and differential equations.
Author | : Jayakumar Ramanathan |
Publisher | : Springer Science & Business Media |
Total Pages | : 334 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461217563 |
Download Methods of Applied Fourier Analysis Book in PDF, ePub and Kindle
Author | : Patrick Flandrin |
Publisher | : Cambridge University Press |
Total Pages | : 231 |
Release | : 2018-09-06 |
Genre | : Technology & Engineering |
ISBN | : 110836912X |
Download Explorations in Time-Frequency Analysis Book in PDF, ePub and Kindle
An authoritative exposition of the methods at the heart of modern non-stationary signal processing from a recognised leader in the field. Offering a global view that favours interpretations and historical perspectives, it explores the basic concepts of time-frequency analysis, and examines the most recent results and developments in the field in the context of existing, lesser-known approaches. Several example waveform families from bioacoustics, mathematics and physics are examined in detail, with the methods for their analysis explained using a wealth of illustrative examples. Methods are discussed in terms of analysis, geometry and statistics. This is an excellent resource for anyone wanting to understand the 'why and how' of important methodological developments in time-frequency analysis, including academics and graduate students in signal processing and applied mathematics, as well as application-oriented scientists.
Author | : Richard Beals |
Publisher | : Springer Nature |
Total Pages | : 353 |
Release | : 2020-10-19 |
Genre | : Mathematics |
ISBN | : 3030545334 |
Download Explorations in Complex Functions Book in PDF, ePub and Kindle
This textbook explores a selection of topics in complex analysis. From core material in the mainstream of complex analysis itself, to tools that are widely used in other areas of mathematics, this versatile compilation offers a selection of many different paths. Readers interested in complex analysis will appreciate the unique combination of topics and connections collected in this book. Beginning with a review of the main tools of complex analysis, harmonic analysis, and functional analysis, the authors go on to present multiple different, self-contained avenues to proceed. Chapters on linear fractional transformations, harmonic functions, and elliptic functions offer pathways to hyperbolic geometry, automorphic functions, and an intuitive introduction to the Schwarzian derivative. The gamma, beta, and zeta functions lead into L-functions, while a chapter on entire functions opens pathways to the Riemann hypothesis and Nevanlinna theory. Cauchy transforms give rise to Hilbert and Fourier transforms, with an emphasis on the connection to complex analysis. Valuable additional topics include Riemann surfaces, steepest descent, tauberian theorems, and the Wiener–Hopf method. Showcasing an array of accessible excursions, Explorations in Complex Functions is an ideal companion for graduate students and researchers in analysis and number theory. Instructors will appreciate the many options for constructing a second course in complex analysis that builds on a first course prerequisite; exercises complement the results throughout.
Author | : J. Marshall Ash |
Publisher | : MAA Press |
Total Pages | : 344 |
Release | : 1976 |
Genre | : Harmonic analysis |
ISBN | : |
Download Studies in Harmonic Analysis Book in PDF, ePub and Kindle
Author | : Camil Muscalu |
Publisher | : Cambridge University Press |
Total Pages | : 341 |
Release | : 2013-01-31 |
Genre | : Mathematics |
ISBN | : 1107031826 |
Download Classical and Multilinear Harmonic Analysis Book in PDF, ePub and Kindle
This contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.