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The International Conference of Computational Harmonic Analysis, held in Hong Kong during the period of June 4 - 8, 2001, brought together mathematicians and engineers interested in the computational aspects of harmonic analysis. Plenary speakers include W Dahmen, R Q Jia, P W Jones, K S Lau, S L Lee, S Smale, J Smoller, G Strang, M Vetterlli, and M V Wickerhauser. The central theme was wavelet analysis in the broadest sense, covering time-frequency and time-scale analysis, filter banks, fast numerical computations, spline methods, multiscale algorithms, approximation theory, signal processing

Wavelets (Mathematics) --- Harmonic analysis

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Analyse harmonique --- Harmonic analysis (Music) --- Harmonische analyse --- Metrum en ritme --- Musical meter and rhythm --- Prosodie et rythme --- harmonisch ritme --- Music --- harmonieleer --- harmonie --- muziektheorie

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An Introduction to Wavelets and Other Filtering Methods in Finance and Economics presents a unified view of filtering techniques with a special focus on wavelet analysis in finance and economics. It emphasizes the methods and explanations of the theory that underlies them. It also concentrates on exactly what wavelet analysis (and filtering methods in general) can reveal about a time series. It offers testing issues which can be performed with wavelets in conjunction with the multi-resolution analysis. The descriptive focus of the book avoids proofs and provides easy access to a wide sp

Finance --- Economics --- Wavelets (Mathematics) --- Econometrics --- Mathematical models --- Econometrics. --- Economics, Mathematical --- Statistics --- Wavelet analysis --- Harmonic analysis --- Mathematical models. --- E-books --- Finances --- Economie politique --- Ondelettes --- Econométrie --- Modèles mathématiques --- Finance - Mathematical models --- Economics - Mathematical models

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Based on a graduate course given by the author at Yale University this book deals with complex analysis (analytic capacity), geometric measure theory (rectifiable and uniformly rectifiable sets) and harmonic analysis (boundedness of singular integral operators on Ahlfors-regular sets). In particular, these notes contain a description of Peter Jones' geometric traveling salesman theorem, the proof of the equivalence between uniform rectifiability and boundedness of the Cauchy operator on Ahlfors-regular sets, the complete proofs of the Denjoy conjecture and the Vitushkin conjecture (for the latter, only the Ahlfors-regular case) and a discussion of X. Tolsa's solution of the Painlevé problem.

Geometric measure theory. --- Capacity theory (Mathematics) --- Harmonic analysis. --- Harmonic analysis --- Mathematical Theory --- Mathematics --- Physical Sciences & Mathematics --- Mathematical analysis. --- Analysis (Mathematics). --- Geometry. --- Measure theory. --- Functions of complex variables. --- Fourier analysis. --- Analysis. --- Measure and Integration. --- Functions of a Complex Variable. --- Fourier Analysis. --- Analysis, Fourier --- Mathematical analysis --- Complex variables --- Elliptic functions --- Functions of real variables --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Euclid's Elements --- 517.1 Mathematical analysis

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This research monograph addresses recent developments of wavelet concepts in the context of large scale numerical simulation. It offers a systematic attempt to exploit the sophistication of wavelets as a numerical tool by adapting wavelet bases to the problem at hand. This includes both the construction of wavelets on fairly general domains and the adaptation of wavelet bases to the particular structure of function spaces governing certain variational problems. Those key features of wavelets that make them a powerful tool in numerical analysis and simulation are clearly pointed out. The particular constructions are guided by the ultimate goal to ensure the key features also for general domains and problem classes. All constructions are illustrated by figures and examples are given.

Mathematical models. --- Wavelets (Mathematics) --- Mathematical models --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- 519.6 --- Computational mathematics. Numerical analysis. Computer programming --- Wavelets (Mathematics). --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Wavelet analysis --- Harmonic analysis --- Models, Mathematical --- Simulation methods --- Numerical analysis. --- Applied mathematics. --- Engineering mathematics. --- Computer mathematics. --- Numerical Analysis. --- Applications of Mathematics. --- Computational Mathematics and Numerical Analysis. --- Computational Science and Engineering. --- Mathematical and Computational Engineering. --- Computer mathematics --- Electronic data processing --- Mathematics --- Engineering --- Engineering analysis --- Mathematical analysis