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This monograph provides a comprehensive overview on a class of nonlinear evolution equations, such as nonlinear Schrödinger equations, nonlinear Klein-Gordon equations, KdV equations as well as Navier-Stokes equations and Boltzmann equations. The global wellposedness to the Cauchy problem for those equations is systematically studied by using the harmonic analysis methods. This book is self-contained and may also be used as an advanced textbook by graduate students in analysis and PDE subjects and even ambitious undergraduate students.

Harmonic analysis. --- Differential equations, Nonlinear. --- Mathematical analysis.

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Wavelets (Mathematics) --- Wavelet analysis --- Harmonic analysis --- Analyse de fourier --- Theorie du signal --- Ondelettes

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L ouvrage commence par pr senter les graphiques pour s ries temporelles offerts par R sur quelques s ries. Il fournit ensuite des rappels de statistique math matique et r vise les concepts et les mod les classiques de s ries. Il pr sente les structures de s ries temporelles dans R et l importation de telles s ries. Il revisite le lissage exponentiel, la lumi re des travaux des 20 derni res ann es sur la question. Un chapitre est consacr la simulation de s ries. Les m thodes sont rapidement illustr es l aide de s ries le plus souvent simul es. On tudie ensuite en d tail six s ries, avec, le plu

Time-series analysis. --- Mathematical statistics. --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Analysis of time series --- Autocorrelation (Statistics) --- Harmonic analysis --- Mathematical statistics --- Statistical methods

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This textbook presents basic notions and techniques of Fourier analysis in discrete settings. Written in a concise style, it is interlaced with remarks, discussions and motivations from signal analysis.   The first part is dedicated to topics related to the Fourier transform, including discrete time-frequency analysis and discrete wavelet analysis. Basic knowledge of linear algebra and calculus is the only prerequisite. The second part is built on Hilbert spaces and Fourier series and culminates in a section on pseudo-differential operators, providing a lucid introduction to this advanced topic in analysis. Some measure theory language is used, although most of this part is accessible to students familiar with an undergraduate course in real analysis.   Discrete Fourier Analysis is aimed at advanced undergraduate and graduate students in mathematics and applied mathematics. Enhanced with exercises, it will be an excellent resource for the classroom as well as for self-study.

Fourier analysis. --- Fourier analysis --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Analysis, Fourier --- Mathematics. --- Harmonic analysis. --- Partial differential equations. --- Numerical analysis. --- Fourier Analysis. --- Abstract Harmonic Analysis. --- Partial Differential Equations. --- Numerical Analysis. --- Mathematical analysis --- Differential equations, partial. --- Partial differential equations --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis

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Since its emergence as an important research area in the early 1980s, the topic of wavelets has undergone tremendous development on both theoretical and applied fronts. Myriad research and survey papers and monographs have been published on the subject, documenting different areas of applications such as sound and image processing, denoising, data compression, tomography, and medical imaging. The study of wavelets remains a very active field of research, and many of its central techniques and ideas have evolved into new and promising research areas. This volume, a collection of invited contributions developed from talks at an international conference on wavelets, features expository and research articles covering current and emerging areas in the theory and applications of wavelets. The book is divided into three parts: Part I is devoted to the mathematical theory of wavelets and features several papers on wavelet sets and the construction of wavelet bases in different settings. Part II looks at the use of multiscale harmonic analysis for understanding the geometry of large data sets and extracting information from them. Part III focuses on applications of wavelet theory to the study of several real-world problems.  Specific topics covered include: wavelets on locally compact groups and Riemannian manifolds;  crystallographic composite dilation wavelets, quincunx and vector-valued  wavelets; multiscale analysis of large data sets; geometric wavelets; wavelets applications in cosmology, atmospheric data analysis and denoising speech signals. Wavelets and Multiscale Analysis: Theory and Applications is an excellent reference for graduate students, researchers, and practitioners in theoretical and applied mathematics, or in engineering.

Electronic books. -- local. --- Engineering mathematics. --- Harmonic analysis. --- Wavelets (Mathematics). --- Wavelets (Mathematics) --- Engineering mathematics --- Harmonic analysis --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Engineering --- Engineering analysis --- Wavelet analysis --- Mathematics --- Mathematics. --- Fourier analysis. --- Applied mathematics. --- Fourier Analysis. --- Signal, Image and Speech Processing. --- Abstract Harmonic Analysis. --- Appl.Mathematics/Computational Methods of Engineering. --- Banach algebras --- Calculus --- Mathematical analysis --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Mathematical and Computational Engineering. --- Analysis, Fourier --- Signal processing. --- Image processing. --- Speech processing systems. --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication)