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Harmonic analysis --- Representations of groups --- Harmonic analysis. --- Representations of groups.

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Boundary element methods --- Harmonic functions --- Marine propellers

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Harmonic functions - the solutions of Laplace's equation - play a crucial role in many areas of mathematics, physics, and engineering. Avoiding the disorganization and inconsistent notation of other expositions, the authors approach the field from a more function-theoretic perspective, emphasizing techniques and results that will seem natural to mathematicians comfortable with complex function theory and harmonic analysis; prerequisites for the book are a solid foundation in real and complex analysis together with some basic results from functional analysis. Topics covered include: basic properties of harmonic functions defined on subsets of Rn, including Poisson integrals; properties bounded functions and positive functions, including Liouville's and Cauchy's theorems; the Kelvin transform; Spherical harmonics; hp theory on the unit ball and on half-spaces; harmonic Bergman spaces; the decomposition theorem; Laurent expansions and classification of isolated singularities; and boundary behavior. An appendix describes routines for use with MATHEMATICA to manipulate some of the expressions that arise in the study of harmonic functions.

Harmonic functions. --- Harmonic functions --- Operations Research --- Applied Mathematics --- Engineering & Applied Sciences --- Civil & Environmental Engineering --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Analysis. --- Global analysis (Mathematics). --- Analyse mathématique --- Mathematical analysis --- Analyse mathématique --- Potentiel, Théorie du --- Fonctions harmoniques

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Designed as an introduction to harmonic analysis and group representations,this book covers a wide range of topics rather than delving deeply into anyparticular one. In the words of H. Weyl ...it is primarily meant forthe humble, who want to learn as new the things set forth therein, rather thanfor the proud and learned who are already familiar with the subject and merelylook for quick and exact information.... The main objective is tointroduce the reader to concepts, ideas, results and techniques that evolvearound symmetry-groups, representations

Analyse harmonique --- Harmonic analysis --- Harmonische analyse --- Representation des groupes --- Representations of groups --- Vertegenwoordiging van groepen --- Analyse harmonique. --- Représentations de groupes. --- Harmonic analysis. --- Representations of groups. --- Représentations de groupes --- 512.54 --- 517.986.6 --- 51-7 --- 512.81 --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Groups. Group theory --- Harmonic analysis of functions of groups and homogeneous spaces --- Mathematical studies and methods in other sciences. Scientific mathematics. Actuarial mathematics. Biometrics. Econometrics etc. --- Lie groups --- 512.81 Lie groups --- 51-7 Mathematical studies and methods in other sciences. Scientific mathematics. Actuarial mathematics. Biometrics. Econometrics etc. --- 517.986.6 Harmonic analysis of functions of groups and homogeneous spaces --- 512.54 Groups. Group theory --- Mathematical studies and methods in other sciences. Scientific mathematics. Actuarial mathematics. Biometrics. Econometrics etc --- Representation of groups.

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Numerical approximation theory --- Wavelets (Mathematics) --- Ondelettes --- 517.518.8 --- 519.6 --- 681.3*G12 --- Wavelet analysis --- Harmonic analysis --- Approximation of functions by polynomials and their generalizations --- Computational mathematics. Numerical analysis. Computer programming --- Approximation: chebyshev; elementary function; least squares; linear approximation; minimax approximation and algorithms; nonlinear and rational approximation; spline and piecewise polynomial approximation (Numerical analysis) --- Wavelets (Mathematics). --- 681.3*G12 Approximation: chebyshev; elementary function; least squares; linear approximation; minimax approximation and algorithms; nonlinear and rational approximation; spline and piecewise polynomial approximation (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 517.518.8 Approximation of functions by polynomials and their generalizations --- Analyse de fourier