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Recent Advances in Harmonic Analysis and Applications

Author: Dmitriy Bilyk

Publisher: Springer Science & Business Media

Published: 2012-10-16

Total Pages: 400

ISBN-13: 1461445647

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.

Recent Advances in Harmonic Analysis and Applications

Author: Dmitriy Bilyk

Publisher: Springer Science & Business Media

Published: 2012-10-16

Total Pages: 400

ISBN-13: 1461445655

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Harmonic Analysis and Applications

Author: Carlos E. Kenig

Publisher: American Mathematical Soc.

Published: 2020-12-14

Total Pages: 345

ISBN-13: 1470461277

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The origins of the harmonic analysis go back to an ingenious idea of Fourier that any reasonable function can be represented as an infinite linear combination of sines and cosines. Today's harmonic analysis incorporates the elements of geometric measure theory, number theory, probability, and has countless applications from data analysis to image recognition and from the study of sound and vibrations to the cutting edge of contemporary physics. The present volume is based on lectures presented at the summer school on Harmonic Analysis. These notes give fresh, concise, and high-level introductions to recent developments in the field, often with new arguments not found elsewhere. The volume will be of use both to graduate students seeking to enter the field and to senior researchers wishing to keep up with current developments.

Harmonic Analysis and Applications

Author: John J. Benedetto

Publisher: CRC Press

Published: 1996-07-29

Total Pages: 370

ISBN-13: 9780849378799

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Harmonic analysis plays an essential role in understanding a host of engineering, mathematical, and scientific ideas. In Harmonic Analysis and Applications, the analysis and synthesis of functions in terms of harmonics is presented in such a way as to demonstrate the vitality, power, elegance, usefulness, and the intricacy and simplicity of the subject. This book is about classical harmonic analysis - a textbook suitable for students, and an essay and general reference suitable for mathematicians, physicists, and others who use harmonic analysis. Throughout the book, material is provided for an upper level undergraduate course in harmonic analysis and some of its applications. In addition, the advanced material in Harmonic Analysis and Applications is well-suited for graduate courses. The course is outlined in Prologue I. This course material is excellent, not only for students, but also for scientists, mathematicians, and engineers as a general reference. Chapter 1 covers the Fourier analysis of integrable and square integrable (finite energy) functions on R. Chapter 2 of the text covers distribution theory, emphasizing the theory's useful vantage point for dealing with problems and general concepts from engineering, physics, and mathematics. Chapter 3 deals with Fourier series, including the Fourier analysis of finite and infinite sequences, as well as functions defined on finite intervals. The mathematical presentation, insightful perspectives, and numerous well-chosen examples and exercises in Harmonic Analysis and Applications make this book well worth having in your collection.

Harmonic Analysis

Author: María Cristina Pereyra

Publisher: American Mathematical Soc.

Published: 2012

Total Pages: 437

ISBN-13: 0821875663

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Conveys the remarkable beauty and applicability of the ideas that have grown from Fourier theory. It presents for an advanced undergraduate and beginning graduate student audience the basics of harmonic analysis, from Fourier's study of the heat equation, and the decomposition of functions into sums of cosines and sines (frequency analysis), to dyadic harmonic analysis, and the decomposition of functions into a Haar basis (time localization).

Advances in Mathematical Finance

Author: Michael C. Fu

Publisher: Springer Science & Business Media

Published: 2007-06-22

Total Pages: 336

ISBN-13: 0817645454

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This self-contained volume brings together a collection of chapters by some of the most distinguished researchers and practitioners in the field of mathematical finance and financial engineering. Presenting state-of-the-art developments in theory and practice, the book has real-world applications to fixed income models, credit risk models, CDO pricing, tax rebates, tax arbitrage, and tax equilibrium. It is a valuable resource for graduate students, researchers, and practitioners in mathematical finance and financial engineering.

Harmonic Analysis and Integral Geometry

Author: Massimo Picardello

Publisher: CRC Press

Published: 2000-09-07

Total Pages: 194

ISBN-13: 9781584881834

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Comprising a selection of expository and research papers, Harmonic Analysis and Integral Geometry grew from presentations offered at the July 1998 Summer University of Safi, Morocco-an annual, advanced research school and congress. This lively and very successful event drew the attendance of many top researchers, who offered both individual lectures and coordinated courses on specific research topics within this fast growing subject. Harmonic Analysis and Integral Geometry presents important recent advances in the fields of Radon transforms, integral geometry, and harmonic analysis on Lie groups and symmetric spaces. Several articles are devoted to the new theory of Radon transforms on trees. With its related presentations addressing recent developments in various aspects of these intriguing areas of study, Harmonic Analysis and Integral Geometry becomes an important addition not only to the Research Notes in Mathematics series, but to the general mathematics literature.

New Trends in Applied Harmonic Analysis, Volume 2

Author: Akram Aldroubi

Publisher: Springer Nature

Published: 2019-11-26

Total Pages: 335

ISBN-13: 3030323536

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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.

Discrete Harmonic Analysis

Author: Tullio Ceccherini-Silberstein

Publisher: Cambridge University Press

Published: 2018-06-21

Total Pages: 589

ISBN-13: 1107182336

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A self-contained introduction to discrete harmonic analysis with an emphasis on the Discrete and Fast Fourier Transforms.

Harmonic Analysis and Applications

Author: Christopher Heil

Publisher: Springer Science & Business Media

Published: 2007-08-02

Total Pages: 390

ISBN-13: 0817645047

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This self-contained volume in honor of John J. Benedetto covers a wide range of topics in harmonic analysis and related areas. These include weighted-norm inequalities, frame theory, wavelet theory, time-frequency analysis, and sampling theory. The chapters are clustered by topic to provide authoritative expositions that will be of lasting interest. The original papers collected are written by prominent researchers and professionals in the field. The book pays tribute to John J. Benedetto’s achievements and expresses an appreciation for the mathematical and personal inspiration he has given to so many students, co-authors, and colleagues.