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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 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 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 2012-05-04 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 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 Analysis and Boundary Value Problems in the Complex Domain by : M.M. Djrbashian
Download or read book Harmonic Analysis and Boundary Value Problems in the Complex Domain written by M.M. Djrbashian and published by Birkhäuser. This book was released on 2012-12-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: As is well known, the first decades of this century were a period of elaboration of new methods in complex analysis. This elaboration had, in particular, one char acteristic feature, consisting in the interfusion of some concepts and methods of harmonic and complex analyses. That interfusion turned out to have great advan tages and gave rise to a vast number of significant results, of which we want to mention especially the classical results on the theory of Fourier series in L2 ( -7r, 7r) and their continual analog - Plancherel's theorem on the Fourier transform in L2 ( -00, +00). We want to note also two important Wiener and Paley theorems on parametric integral representations of a subclass of entire functions of expo nential type in the Hardy space H2 over a half-plane. Being under the strong influence of these results, the author began in the fifties a series of investigations in the theory of integral representations of analytic and entire functions as well as in the theory of harmonic analysis in the com plex domain. These investigations were based on the remarkable properties of the asymptotics of the entire function (p, J1 > 0), which was introduced into mathematical analysis by Mittag-Leffler for the case J1 = 1. In the process of investigation, the scope of some classical results was essentially enlarged, and the results themselves were evaluated.
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 Harmonic and Applied Analysis by : Filippo De Mari
Download or read book Harmonic and Applied Analysis written by Filippo De Mari and published by Birkhäuser. This book was released on 2022-12-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
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 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 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 Introduction to Abstract Harmonic Analysis by : Lynn H. Loomis
Download or read book Introduction to Abstract Harmonic Analysis written by Lynn H. Loomis and published by Courier Corporation. This book was released on 2013-05-09 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a prominent figure in the field of harmonic analysis, this classic monograph is geared toward advanced undergraduates and graduate students and focuses on methods related to Gelfand's theory of Banach algebra. 1953 edition.
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 160 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 Theories and Practice of Harmonic Analysis by : Gene J. Cho
Download or read book Theories and Practice of Harmonic Analysis written by Gene J. Cho and published by Emtext. This book was released on 1992 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume brings together information regarding the theories of harmonic analysis. It provides a list of concerns and proposes procedural perspectives and recommendations for analysis and for harmonic analysis in particular. It is also a critical review and reassessment of Gottfried Weber's contribution to harmonic analysis and demonstrates proper application of Weber's analytic system. The text is augmented by over 60 musical examples.
Book Synopsis Harmonic and Complex Analysis in Several Variables by : Steven G. Krantz
Download or read book Harmonic and Complex Analysis in Several Variables written by Steven G. Krantz and published by Springer. This book was released on 2017-09-20 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Authored by a ranking authority in harmonic analysis of several complex variables, this book embodies a state-of-the-art entrée at the intersection of two important fields of research: complex analysis and harmonic analysis. Written with the graduate student in mind, it is assumed that the reader has familiarity with the basics of complex analysis of one and several complex variables as well as with real and functional analysis. The monograph is largely self-contained and develops the harmonic analysis of several complex variables from the first principles. The text includes copious examples, explanations, an exhaustive bibliography for further reading, and figures that illustrate the geometric nature of the subject. Each chapter ends with an exercise set. Additionally, each chapter begins with a prologue, introducing the reader to the subject matter that follows; capsules presented in each section give perspective and a spirited launch to the segment; preludes help put ideas into context. Mathematicians and researchers in several applied disciplines will find the breadth and depth of the treatment of the subject highly useful.
