Harmonic And Applied Analysis

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Harmonic and Applied Analysis

Filippo De Mari,Ernesto De Vito
Harmonic and Applied Analysis Book PDF

Author : Filippo De Mari,Ernesto De Vito
Publisher : Birkhäuser
Page : 0 pages
File Size : 54,7 Mb
Release : 2022-12-15
Category : Mathematics
ISBN : 3030866661

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Harmonic and Applied Analysis by Filippo De Mari,Ernesto De Vito Pdf

Deep connections exist between harmonic and applied analysis and the diverse yet connected topics of machine learning, data analysis, and imaging science. This volume explores these rapidly growing areas and features contributions presented at the second and third editions of the Summer Schools on Applied Harmonic Analysis, held at the University of Genova in 2017 and 2019. Each chapter offers an introduction to essential material and then demonstrates connections to more advanced research, with the aim of providing an accessible entrance for students and researchers. Topics covered include ill-posed problems; concentration inequalities; regularization and large-scale machine learning; unitarization of the radon transform on symmetric spaces; and proximal gradient methods for machine learning and imaging.

Harmonic and Applied Analysis

Stephan Dahlke,Filippo De Mari,Philipp Grohs,Demetrio Labate
Harmonic and Applied Analysis Book PDF

Author : Stephan Dahlke,Filippo De Mari,Philipp Grohs,Demetrio Labate
Publisher : Birkhäuser
Page : 256 pages
File Size : 50,7 Mb
Release : 2015-09-12
Category : Mathematics
ISBN : 9783319188638

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Harmonic and Applied Analysis by Stephan Dahlke,Filippo De Mari,Philipp Grohs,Demetrio Labate Pdf

This contributed volume explores the connection between the theoretical aspects of harmonic analysis and the construction of advanced multiscale representations that have emerged in signal and image processing. It highlights some of the most promising mathematical developments in harmonic analysis in the last decade brought about by the interplay among different areas of abstract and applied mathematics. This intertwining of ideas is considered starting from the theory of unitary group representations and leading to the construction of very efficient schemes for the analysis of multidimensional data. After an introductory chapter surveying the scientific significance of classical and more advanced multiscale methods, chapters cover such topics as An overview of Lie theory focused on common applications in signal analysis, including the wavelet representation of the affine group, the Schrödinger representation of the Heisenberg group, and the metaplectic representation of the symplectic group An introduction to coorbit theory and how it can be combined with the shearlet transform to establish shearlet coorbit spaces Microlocal properties of the shearlet transform and its ability to provide a precise geometric characterization of edges and interface boundaries in images and other multidimensional data Mathematical techniques to construct optimal data representations for a number of signal types, with a focus on the optimal approximation of functions governed by anisotropic singularities. A unified notation is used across all of the chapters to ensure consistency of the mathematical material presented. Harmonic and Applied Analysis: From Groups to Signals is aimed at graduate students and researchers in the areas of harmonic analysis and applied mathematics, as well as at other applied scientists interested in representations of multidimensional data. It can also be used as a textbook for graduate courses in applied harmonic analysis.​

Harmonic Analysis and Applications

Carlos E. Kenig
Harmonic Analysis and Applications Book PDF

Author : Carlos E. Kenig
Publisher : American Mathematical Soc.
Page : 345 pages
File Size : 41,8 Mb
Release : 2020-12-14
Category : Education
ISBN : 9781470461270

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Harmonic Analysis and Applications by Carlos E. Kenig Pdf

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.

Advances in Mathematical Finance

Michael C. Fu,Robert A. Jarrow,Ju-Yi Yen,Robert J Elliott
Advances in Mathematical Finance Book PDF

Author : Michael C. Fu,Robert A. Jarrow,Ju-Yi Yen,Robert J Elliott
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 47,8 Mb
Release : 2007-06-22
Category : Business & Economics
ISBN : 9780817645458

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Advances in Mathematical Finance by Michael C. Fu,Robert A. Jarrow,Ju-Yi Yen,Robert J Elliott Pdf

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.

Methods of Applied Mathematics with a MATLAB Overview

Jon H. Davis
Methods of Applied Mathematics with a MATLAB Overview Book PDF

Author : Jon H. Davis
Publisher : Springer Science & Business Media
Page : 744 pages
File Size : 45,9 Mb
Release : 2004
Category : Mathematics
ISBN : 0817643311

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Methods of Applied Mathematics with a MATLAB Overview by Jon H. Davis Pdf

Broadly organized around the applications of Fourier analysis, "Methods of Applied Mathematics with a MATLAB Overview" covers both classical applications in partial differential equations and boundary value problems, as well as the concepts and methods associated to the Laplace, Fourier, and discrete transforms. Transform inversion problems are also examined, along with the necessary background in complex variables. A final chapter treats wavelets, short-time Fourier analysis, and geometrically-based transforms. The computer program MATLAB is emphasized throughout, and an introduction to MATLAB is provided in an appendix. Rich in examples, illustrations, and exercises of varying difficulty, this text can be used for a one- or two-semester course and is ideal for students in pure and applied mathematics, physics, and engineering.

Harmonic Analysis for Engineers and Applied Scientists

Gregory S. Chirikjian,Alexander B. Kyatkin
Harmonic Analysis for Engineers and Applied Scientists Book PDF

Author : Gregory S. Chirikjian,Alexander B. Kyatkin
Publisher : Courier Dover Publications
Page : 881 pages
File Size : 41,7 Mb
Release : 2016-07-20
Category : Mathematics
ISBN : 9780486795645

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Harmonic Analysis for Engineers and Applied Scientists by Gregory S. Chirikjian,Alexander B. Kyatkin Pdf

Although the Fourier transform is among engineering's most widely used mathematical tools, few engineers realize that the extension of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. This self-contained approach, geared toward readers with a standard background in engineering mathematics, explores the widest possible range of applications to fields such as robotics, mechanics, tomography, sensor calibration, estimation and control, liquid crystal analysis, and conformational statistics of macromolecules. Harmonic analysis is explored in terms of particular Lie groups, and the text deals with only a limited number of proofs, focusing instead on specific applications and fundamental mathematical results. Forming a bridge between pure mathematics and the challenges of modern engineering, this updated and expanded volume offers a concrete, accessible treatment that places the general theory in the context of specific groups.

Harmonic and Applied Analysis

Filippo De Mari,Ernesto De Vito
Harmonic and Applied Analysis Book PDF

Author : Filippo De Mari,Ernesto De Vito
Publisher : Springer Nature
Page : 316 pages
File Size : 40,6 Mb
Release : 2021-12-13
Category : Mathematics
ISBN : 9783030866648

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Harmonic and Applied Analysis by Filippo De Mari,Ernesto De Vito Pdf

Deep connections exist between harmonic and applied analysis and the diverse yet connected topics of machine learning, data analysis, and imaging science. This volume explores these rapidly growing areas and features contributions presented at the second and third editions of the Summer Schools on Applied Harmonic Analysis, held at the University of Genova in 2017 and 2019. Each chapter offers an introduction to essential material and then demonstrates connections to more advanced research, with the aim of providing an accessible entrance for students and researchers. Topics covered include ill-posed problems; concentration inequalities; regularization and large-scale machine learning; unitarization of the radon transform on symmetric spaces; and proximal gradient methods for machine learning and imaging.

Harmonic Analysis on Free Groups

Figa-Talamanca
Harmonic Analysis on Free Groups Book PDF

Author : Figa-Talamanca
Publisher : CRC Press
Page : 164 pages
File Size : 50,5 Mb
Release : 1983-08-17
Category : Mathematics
ISBN : 0824770420

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Harmonic Analysis on Free Groups by Figa-Talamanca Pdf

This book presents an account of recent results on the theory of representations and the harmonic analysis of free groups. It emphasizes the analogy with the theory of representations of noncompact semisimple Lie groups and restricts the focus to a class of irreducible unitary representations.

New Trends in Applied Harmonic Analysis, Volume 2

Akram Aldroubi,Carlos Cabrelli,Stéphane Jaffard,Ursula Molter
New Trends in Applied Harmonic Analysis Volume 2 Book PDF

Author : Akram Aldroubi,Carlos Cabrelli,Stéphane Jaffard,Ursula Molter
Publisher : Springer Nature
Page : 335 pages
File Size : 46,7 Mb
Release : 2019-11-26
Category : Mathematics
ISBN : 9783030323530

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New Trends in Applied Harmonic Analysis, Volume 2 by Akram Aldroubi,Carlos Cabrelli,Stéphane Jaffard,Ursula Molter Pdf

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.

Harmonic Analysis, Signal Processing, and Complexity

Irene Sabadini,Daniele C. Struppa,David F. Walnut
Harmonic Analysis Signal Processing and Complexity Book PDF

Author : Irene Sabadini,Daniele C. Struppa,David F. Walnut
Publisher : Springer Science & Business Media
Page : 172 pages
File Size : 44,8 Mb
Release : 2008-12-16
Category : Mathematics
ISBN : 9780817644161

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Harmonic Analysis, Signal Processing, and Complexity by Irene Sabadini,Daniele C. Struppa,David F. Walnut Pdf

* Original articles and survey articles in honor of the sixtieth birthday of Carlos A. Berenstein reflect his diverse research interests from interpolation to residue theory to deconvolution and its applications to issues ranging from optics to the study of blood flow * Contains both theoretical papers in harmonic and complex analysis, as well as more applied work in signal processing * Top-notch contributors in their respective fields

Harmonic Analysis and Applications

John J. Benedetto
Harmonic Analysis and Applications Book PDF

Author : John J. Benedetto
Publisher : CRC Press
Page : 370 pages
File Size : 51,7 Mb
Release : 1996-07-29
Category : Mathematics
ISBN : 0849378796

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Harmonic Analysis and Applications by John J. Benedetto Pdf

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 on Homogeneous Spaces

Nolan R. Wallach
Harmonic Analysis on Homogeneous Spaces Book PDF

Author : Nolan R. Wallach
Publisher : Courier Dover Publications
Page : 384 pages
File Size : 42,9 Mb
Release : 2018-12-12
Category : Mathematics
ISBN : 9780486836430

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Harmonic Analysis on Homogeneous Spaces by Nolan R. Wallach Pdf

This book is suitable for advanced undergraduate and graduate students in mathematics with a strong background in linear algebra and advanced calculus. Early chapters develop representation theory of compact Lie groups with applications to topology, geometry, and analysis, including the Peter-Weyl theorem, the theorem of the highest weight, the character theory, invariant differential operators on homogeneous vector bundles, and Bott's index theorem for such operators. Later chapters study the structure of representation theory and analysis of non-compact semi-simple Lie groups, including the principal series, intertwining operators, asymptotics of matrix coefficients, and an important special case of the Plancherel theorem. Teachers will find this volume useful as either a main text or a supplement to standard one-year courses in Lie groups and Lie algebras. The treatment advances from fairly simple topics to more complex subjects, and exercises appear at the end of each chapter. Eight helpful Appendixes develop aspects of differential geometry, Lie theory, and functional analysis employed in the main text.

Recent Advances in Harmonic Analysis and Applications

Dmitriy Bilyk,Laura De Carli,Alexander Petukhov,Alexander M. Stokolos,Brett D. Wick
Recent Advances in Harmonic Analysis and Applications Book PDF

Author : Dmitriy Bilyk,Laura De Carli,Alexander Petukhov,Alexander M. Stokolos,Brett D. Wick
Publisher : Springer Science & Business Media
Page : 400 pages
File Size : 47,7 Mb
Release : 2012-10-16
Category : Mathematics
ISBN : 9781461445647

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Recent Advances in Harmonic Analysis and Applications by Dmitriy Bilyk,Laura De Carli,Alexander Petukhov,Alexander M. Stokolos,Brett D. Wick Pdf

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.

Principles of Harmonic Analysis

Anton Deitmar,Siegfried Echterhoff
Principles of Harmonic Analysis Book PDF

Author : Anton Deitmar,Siegfried Echterhoff
Publisher : Springer
Page : 332 pages
File Size : 53,8 Mb
Release : 2014-06-21
Category : Mathematics
ISBN : 9783319057927

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Principles of Harmonic Analysis by Anton Deitmar,Siegfried Echterhoff Pdf

This book offers a complete and streamlined treatment of the central principles of abelian harmonic analysis: Pontryagin duality, the Plancherel theorem and the Poisson summation formula, as well as their respective generalizations to non-abelian groups, including the Selberg trace formula. The principles are then applied to spectral analysis of Heisenberg manifolds and Riemann surfaces. This new edition contains a new chapter on p-adic and adelic groups, as well as a complementary section on direct and projective limits. Many of the supporting proofs have been revised and refined. The book is an excellent resource for graduate students who wish to learn and understand harmonic analysis and for researchers seeking to apply it.

Harmonic Analysis and Applications

Christopher Heil
Harmonic Analysis and Applications Book PDF

Author : Christopher Heil
Publisher : Springer Science & Business Media
Page : 390 pages
File Size : 40,8 Mb
Release : 2007-08-02
Category : Mathematics
ISBN : 9780817645045

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Harmonic Analysis and Applications by Christopher Heil Pdf

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.