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Twentieth Century Harmonic Analysis
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Book Synopsis Twentieth Century Harmonic Analysis by : J.S. Byrnes
Download or read book Twentieth Century Harmonic Analysis written by J.S. Byrnes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: Almost a century ago, harmonic analysis entered a (still continuing) Golden Age, with the emergence of many great masters throughout Europe. They created a wealth of profound analytic methods, to be successfully exploited and further developed by succeeding generations. This flourishing of harmonic analysis is today as lively as ever, as the papers presented here demonstrate. In addition to its own ongoing internal development and its basic role in other areas of mathematics, physics and chemistry, financial analysis, medicine, and biological signal processing, harmonic analysis has made fundamental contributions to essentially all twentieth century technology-based human endeavours, including telephone, radio, television, radar, sonar, satellite communications, medical imaging, the Internet, and multimedia. This ubiquitous nature of the subject is amply illustrated. The book not only promotes the infusion of new mathematical tools into applied harmonic analysis, but also to fuel the development of applied mathematics by providing opportunities for young engineers, mathematicians and other scientists to learn more about problem areas in today's technology that might benefit from new mathematical insights.
Book Synopsis Music and Twentieth-century Tonality by : Paolo Susanni
Download or read book Music and Twentieth-century Tonality written by Paolo Susanni and published by Routledge. This book was released on 2012 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the web of pitch relations that generates the musical language of non-serialized twelve-tone music and supplies both the analytical materials and methods necessary for analyses of a vast proportion of the 20th century musical repertoire. It does so in a simple, clear, and systematic manner to promote an easily accessible and global understanding of this music. Since the chromatic scale is the primary source for the pitch materials of 20th-century music, common sub-collections of the various modes and interval cycles serve as the basis for their mutual transformation. It is precisely this peculiarity of the non-serialized twelve-tone system that allows for an array of pitch relations and modal techniques hitherto perceived difficult if not impossible to analyze. Susanni and Antokoletz present the principles, concepts, and materials employed for analysis using a unique theoretic-analytical approach to the new musical language. The book contains a large number of original analyses that explore a host of composers including Ives, Stravinsky, Bartók, Messiaen, Cage, Debussy, Copland, and many more, providing insight into the music of the tonal revolution of the twentieth century and contributing an important perspective to how music works in general.
Book Synopsis Harmonic Analysis on Spaces of Homogeneous Type by : Donggao Deng
Download or read book Harmonic Analysis on Spaces of Homogeneous Type written by Donggao Deng and published by Springer Science & Business Media. This book was released on 2008-11-19 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book could have been entitled “Analysis and Geometry.” The authors are addressing the following issue: Is it possible to perform some harmonic analysis on a set? Harmonic analysis on groups has a long tradition. Here we are given a metric set X with a (positive) Borel measure ? and we would like to construct some algorithms which in the classical setting rely on the Fourier transformation. Needless to say, the Fourier transformation does not exist on an arbitrary metric set. This endeavor is not a revolution. It is a continuation of a line of research whichwasinitiated,acenturyago,withtwofundamentalpapersthatIwould like to discuss brie?y. The ?rst paper is the doctoral dissertation of Alfred Haar, which was submitted at to University of Gottingen ̈ in July 1907. At that time it was known that the Fourier series expansion of a continuous function may diverge at a given point. Haar wanted to know if this phenomenon happens for every 2 orthonormal basis of L [0,1]. He answered this question by constructing an orthonormal basis (today known as the Haar basis) with the property that the expansion (in this basis) of any continuous function uniformly converges to that function.
Book Synopsis Harmonic Analysis and Applications by : Christopher Heil
Download or read book Harmonic Analysis and Applications written by Christopher Heil and published by Springer Science & Business Media. This book was released on 2007-08-02 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Twentieth Century Harmony by : Vincent Persichetti
Download or read book Twentieth Century Harmony written by Vincent Persichetti and published by London : Faber & Faber. This book was released on 1961 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Music for Analysis by : Thomas Benjamin
Download or read book Music for Analysis written by Thomas Benjamin and published by . This book was released on 2009-10-08 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: Music for Analysis is a varied collection of more than 400 pieces of music from the Baroque period to the present. This anthology provides both excerpts and complete pieces for analysis of style, musical idiom, small forms, tonal harmony, and contemporary techniques. Covering a full range of genres, styles, media, and composers, the musical pieces illustrate standard usage and idiomatic procedures and can be used with any music theory text. Organized logically by harmonic content, Music for Analysis moves progressively and systematically through the techniques and musical scores of the common practice period and 20th century. In the Sixth Edition, the authors have placed more emphasis on the complete pieces for analysis already included and added several more (including Gavea by Darius Milhaud, which contains a wide variety of contemporary techniques, and a complete Mozart sonata). The revision also includes precise measure numbers for all excerpts from larger pieces. In this new edition, an audio CD containing recorded music from the text will be packaged with each book.
Book Synopsis Tonal Harmony, with an Introduction to Twentieth-century Music by : Stefan M. Kostka
Download or read book Tonal Harmony, with an Introduction to Twentieth-century Music written by Stefan M. Kostka and published by Alfred A. Knopf. This book was released on 1989 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Excursions in Harmonic Analysis, Volume 6 by : Matthew Hirn
Download or read book Excursions in Harmonic Analysis, Volume 6 written by Matthew Hirn and published by Springer Nature. This book was released on 2021-09-01 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Music for Analysis by : Thomas Benjamin
Download or read book Music for Analysis written by Thomas Benjamin and published by Oxford University Press, USA. This book was released on 2018-01-16 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt: With over 475 pieces of music from the Baroque period to the present, this is the most comprehensive anthology of its kind. Organized by music theory concept, it can be easily adapted to any introductory theory course, plus ample room for student work eliminates the need for a separateworkbook or score paper.
Book Synopsis Gaussian Harmonic Analysis by : Wilfredo Urbina-Romero
Download or read book Gaussian Harmonic Analysis written by Wilfredo Urbina-Romero and published by Springer. This book was released on 2019-06-21 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: Authored by a ranking authority in Gaussian harmonic analysis, this book embodies a state-of-the-art entrée at the intersection of two important fields of research: harmonic analysis and probability. The book is intended for a very diverse audience, from graduate students all the way to researchers working in a broad spectrum of areas in analysis. Written with the graduate student in mind, it is assumed that the reader has familiarity with the basics of real analysis as well as with classical harmonic analysis, including Calderón-Zygmund theory; also some knowledge of basic orthogonal polynomials theory would be convenient. The monograph develops the main topics of classical harmonic analysis (semigroups, covering lemmas, maximal functions, Littlewood-Paley functions, spectral multipliers, fractional integrals and fractional derivatives, singular integrals) with respect to the Gaussian measure. The text provide an updated exposition, as self-contained as possible, of all the topics in Gaussian harmonic analysis that up to now are mostly scattered in research papers and sections of books; also an exhaustive bibliography for further reading. Each chapter ends with a section of notes and further results where connections between Gaussian harmonic analysis and other connected fields, points of view and alternative techniques are given. Mathematicians and researchers in several areas will find the breadth and depth of the treatment of the subject highly useful.
Book Synopsis Principles of Harmonic Analysis by : Anton Deitmar
Download or read book Principles of Harmonic Analysis written by Anton Deitmar and published by Springer. This book was released on 2014-06-21 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Harmonic Analysis on Spaces of Homogeneous Type by : Donggao Deng
Download or read book Harmonic Analysis on Spaces of Homogeneous Type written by Donggao Deng and published by Springer. This book was released on 2008-11-21 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book could have been entitled “Analysis and Geometry.” The authors are addressing the following issue: Is it possible to perform some harmonic analysis on a set? Harmonic analysis on groups has a long tradition. Here we are given a metric set X with a (positive) Borel measure ? and we would like to construct some algorithms which in the classical setting rely on the Fourier transformation. Needless to say, the Fourier transformation does not exist on an arbitrary metric set. This endeavor is not a revolution. It is a continuation of a line of research whichwasinitiated,acenturyago,withtwofundamentalpapersthatIwould like to discuss brie?y. The ?rst paper is the doctoral dissertation of Alfred Haar, which was submitted at to University of Gottingen ̈ in July 1907. At that time it was known that the Fourier series expansion of a continuous function may diverge at a given point. Haar wanted to know if this phenomenon happens for every 2 orthonormal basis of L [0,1]. He answered this question by constructing an orthonormal basis (today known as the Haar basis) with the property that the expansion (in this basis) of any continuous function uniformly converges to that function.
Book Synopsis Harmonic Analysis and Partial Differential Equations by : Alberto P. Calderón
Download or read book Harmonic Analysis and Partial Differential Equations written by Alberto P. Calderón and published by University of Chicago Press. This book was released on 1999 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Alberto P. Calderón (1920-1998) was one of this century's leading mathematical analysts. His contributions, characterized by great originality and depth, have changed the way researchers approach and think about everything from harmonic analysis to partial differential equations and from signal processing to tomography. In addition, he helped define the "Chicago school" of analysis, which remains influential to this day. In 1996, more than 300 mathematicians from around the world gathered in Chicago for a conference on harmonic analysis and partial differential equations held in Calderón's honor. This volume originated in papers given there and presents timely syntheses of several major fields of mathematics as well as original research articles contributed by some of the finest scholars working in these areas. An important addition to the literature, this book is essential reading for researchers in these and other related fields.
Book Synopsis Harmonic and Applied Analysis by : Stephan Dahlke
Download or read book Harmonic and Applied Analysis written by Stephan Dahlke and published by Birkhäuser. This book was released on 2015-09-12 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Theory of Axis-tonality for Twentieth-century Music by : Richard A. Chrisman
Download or read book A Theory of Axis-tonality for Twentieth-century Music written by Richard A. Chrisman and published by . This book was released on 1969 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Historical Treatise of Harmonic Analysis by : Jacques Chailley
Download or read book Historical Treatise of Harmonic Analysis written by Jacques Chailley and published by . This book was released on 1986 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Panorama of Hungarian Mathematics in the Twentieth Century, I by : Janos Horvath
Download or read book A Panorama of Hungarian Mathematics in the Twentieth Century, I written by Janos Horvath and published by Springer Science & Business Media. This book was released on 2010-06-28 with total page 639 pages. Available in PDF, EPUB and Kindle. Book excerpt: A glorious period of Hungarian mathematics started in 1900 when Lipót Fejér discovered the summability of Fourier series.This was followed by the discoveries of his disciples in Fourier analysis and in the theory of analytic functions. At the same time Frederic (Frigyes) Riesz created functional analysis and Alfred Haar gave the first example of wavelets. Later the topics investigated by Hungarian mathematicians broadened considerably, and included topology, operator theory, differential equations, probability, etc. The present volume, the first of two, presents some of the most remarkable results achieved in the twentieth century by Hungarians in analysis, geometry and stochastics. The book is accessible to anyone with a minimum knowledge of mathematics. It is supplemented with an essay on the history of Hungary in the twentieth century and biographies of those mathematicians who are no longer active. A list of all persons referred to in the chapters concludes the volume.
