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Titlebook: Wavelets, Approximation, and Statistical Applications; Wolfgang Härdle,Gerard Kerkyacharian,Alexander Tsy Book 1998 Springer-Verlag New Yo

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书目名称Wavelets, Approximation, and Statistical Applications
编辑Wolfgang Härdle,Gerard Kerkyacharian,Alexander Tsy
视频video
丛书名称Lecture Notes in Statistics
图书封面Titlebook: Wavelets, Approximation, and Statistical Applications;  Wolfgang Härdle,Gerard Kerkyacharian,Alexander Tsy Book 1998 Springer-Verlag New Yo
描述The mathematical theory of ondelettes (wavelets) was developed by Yves Meyer and many collaborators about 10 years ago. It was designed for ap­ proximation of possibly irregular functions and surfaces and was successfully applied in data compression, turbulence analysis, image and signal process­ ing. Five years ago wavelet theory progressively appeared to be a power­ ful framework for nonparametric statistical problems. Efficient computa­ tional implementations are beginning to surface in this second lustrum of the nineties. This book brings together these three main streams of wavelet theory. It presents the theory, discusses approximations and gives a variety of statistical applications. It is the aim of this text to introduce the novice in this field into the various aspects of wavelets. Wavelets require a highly interactive computing interface. We present therefore all applications with software code from an interactive statistical computing environment. Readers interested in theory and construction of wavelets will find here in a condensed form results that are somewhat scattered around in the research literature. A practioner will be able to use wavelets via the available so
出版日期Book 1998
关键词DEX; Invariant; Lemma; Oracle; Sequence space; Sobolev space; adaptation; availability; code; construction; fu
版次1
doihttps://doi.org/10.1007/978-1-4612-2222-4
isbn_softcover978-0-387-98453-7
isbn_ebook978-1-4612-2222-4Series ISSN 0930-0325 Series E-ISSN 2197-7186
issn_series 0930-0325
copyrightSpringer-Verlag New York, Inc. 1998
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The Haar basis wavelet system,The Haar basis is known since 1910. Here we consider the Haar basis on the real line . and describe some of its properties which are useful for the construction of general wavelet systems. Let . (.) be the space of all complex valued functions . on . such that their .-norm is finite:
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Some facts from Fourier analysis,This small chapter is here to summarize the classical facts of Fourier analysis that will be used in the sequel. We omit the proofs (except for the Poisson summation formula). They can be found in standard textbooks on the subject, for instance in Katznelson (1976), Stein & Weiss (1971).
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