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Algebraische Geometrie. --- Fourier analysis. --- Fourier transformations. --- Integraltransformation --- Integraltransformation. --- Algebraische Geometrie.

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The primary goal of these two volumes is to present the theoretical foundation of the field of Euclidean Harmonic analysis. The original edition was published as a single volume, but due to its size, scope, and the addition of new material, the second edition consists of two volumes. The present edition contains a new chapter on time-frequency analysis and the Carleson-Hunt theorem. The first volume contains the classical topics such as Interpolation, Fourier Series, the Fourier Transform, Maximal Functions, Singular Integrals, and Littlewood-Paley Theory. The second volume contains more recent topics such as Function Spaces, Atomic Decompositions, Singular Integrals of Nonconvolution Type, and Weighted Inequalities. These volumes are mainly addressed to graduate students in mathematics and are designed for a two-course sequence on the subject with additional material included for reference. The prerequisites for the first volume are satisfactory completion of courses in real and complex variables. The second volume assumes material from the first. This book is intended to present the selected topics in depth and stimulate further study. Although the emphasis falls on real variable methods in Euclidean spaces, a chapter is devoted to the fundamentals of analysis on the torus. This material is included for historical reasons, as the genesis of Fourier analysis can be found in trigonometric expansions of periodic functions in several variables. About the first edition: "Grafakos's book is very user-friendly with numerous examples illustrating the definitions and ideas... The treatment is thoroughly modern with free use of operators and functional analysis. Morever, unlike many authors, Grafakos has clearly spent a great deal of time preparing the exercises." - Kenneth Ross, MAA Online.

Fourier analysis. --- Fourier analysis --- Operations Research --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Analysis, Fourier --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Harmonic analysis. --- Functional analysis. --- Analysis. --- Fourier Analysis. --- Abstract Harmonic Analysis. --- Functional Analysis. --- Mathematical analysis --- Harmonic analysis --- Global analysis (Mathematics). --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- 517.1 Mathematical analysis --- Analyse harmonique (mathématiques) --- Groupes topologiques --- Analyse harmonique (mathématiques) --- Représentations de groupes

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Acoustics and the Performance of Music connects scientific understandings of acoustics with practical applications to musical performance. Of central importance are the tonal characteristics of musical instruments and the singing voice including detailed representations of directional characteristics. Furthermore, room acoustical concerns related to concert halls and opera houses are considered. Based on this, suggestions are made for musical performance. Included are seating arrangements within the orchestra and adaptations of performance techniques to the performance environment. In the presentation we dispense with complicated mathematical connections and deliberately aim for conceptual explanations accessible to musicians, particularly for conductors. The graphical representations of the directional dependence of sound radiation by musical instruments and the singing voice are unique. Since the first edition was published in 1978, this book has been completely revised and rewritten to include current research. This translation corresponds to the latest (fifth) German edition (2004), which has become a standard reference work for audio engineers and scientists. Acoustics and the Performance of Music addresses issues that are of interest to acousticians, orchestra performers and conductors, audio engineers, architects. Researchers and students of musical acoustics will also find this text valuable.

Acoustical engineering. --- Conducting. --- Harmonic analysis --Congresses. --- Lie algebras --Congresses. --- Lie groups --Congresses. --- Music --Acoustics and physics. --- Music --Performance. --- Theaters --Acoustic properties. --- Music --- Acoustical engineering --- Conducting --- Theaters --- Acoustics & Sound --- Music Philosophy --- Physics --- Music, Dance, Drama & Film --- Physical Sciences & Mathematics --- Acoustics and physics --- Performance --- Acoustic properties --- Acoustics and physics. --- Performance. --- Acoustic properties. --- Opera-houses --- Playhouses (Theaters) --- Theatres --- Acoustic engineering --- Sonic engineering --- Sonics --- Sound engineering --- Sound-waves --- Musical acoustics --- Musical performance --- Performance of music --- Band conducting --- Conducting (Music) --- Music conducting --- Orchestra conducting --- Industrial applications --- Physics. --- Acoustics. --- Engineering Acoustics. --- 517 <061.3> --- 517.9 --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- 517 <061.3> Analysis--?<061.3> --- Analysis--?<061.3> --- Harmonic analysis. Fourier analysis --- Ergodic theory. Information theory --- 519.2 --- 519.2 Probability. Mathematical statistics --- Probability. Mathematical statistics --- Engineering --- Arts facilities --- Auditoriums --- Centers for the performing arts --- Music-halls --- Sound --- Monochord --- Harmonic analysis --- Lie algebras --- Lie groups --- Congresses. --- Ergodic theory --- Topological dynamics --- Acoustics in engineering. --- Théorie ergodique --- Théorie ergodique. --- Systèmes dynamiques --- Systèmes dynamiques --- Théorie ergodique --- Analyse harmonique