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Titlebook: Wavelet Transforms and Localization Operators; M. W. Wong Book 2002 Springer Basel AG 2002 functional analysis.harmonic analysis.mathemati

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发表于 2025-3-21 17:29:58 | 显示全部楼层 |阅读模式
书目名称Wavelet Transforms and Localization Operators
编辑M. W. Wong
视频video
丛书名称Operator Theory: Advances and Applications
图书封面Titlebook: Wavelet Transforms and Localization Operators;  M. W. Wong Book 2002 Springer Basel AG 2002 functional analysis.harmonic analysis.mathemati
描述This book is based on lectures given at the Global Analysis Research Center (GARC) of Seoul National University in 1999and at Peking University in 1999and 2000. Preliminary versions of the book have been used for various topics courses in analysis for graduate students at York University. We study in this book wavelet transforms and localization operators in the context of infinite-dimensional and square-integrable representations of locally compact and Hausdorffgroups. The wavelet transforms studied in this book, which include the ones that come from the Weyl-Heisenberg group and the well-known affine group, are the building blocks of localization operators. The theme that dominates the book is the spectral theory of wavelet transforms and localization operators in the form of Schatten-von Neumann norm inequalities. Several chap­ ters are also devoted to the product formulas for concrete localization operators such as Daubechies operators and wavelet multipliers. This book is a natural sequel to the book on pseudo-differential operators [103] and the book on Weyl transforms [102] by the author. Indeed, localization operators on the Weyl-Heisenberg group are Weyl transforms, which
出版日期Book 2002
关键词functional analysis; harmonic analysis; mathematical physics; measure; operator theory; signal analysis; w
版次1
doihttps://doi.org/10.1007/978-3-0348-8217-0
isbn_softcover978-3-0348-9478-4
isbn_ebook978-3-0348-8217-0Series ISSN 0255-0156 Series E-ISSN 2296-4878
issn_series 0255-0156
copyrightSpringer Basel AG 2002
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发表于 2025-3-21 20:25:34 | 显示全部楼层
Schatten-von Neumann Classes,way that we can use them easily later in this book. Some proofs are omitted whenever they are easily available in the literature. More comprehensive accounts on the Schatten-von Neumann classes can be found in Dunford and Schwartz [25], Gohberg, Goldberg and Krupnik [31], Reed and Simon [72], Simon
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Topological Groups,ons, which we give in the next chapter. Basic references include Folland [27] and Pontryagin [68]. The book [45] is a good reference for the basic group theory used in this book. As for general topology, the books [54] and [64] by Kelley and Munkres respectively are standard references.
发表于 2025-3-22 12:39:57 | 显示全部楼层
Unitary Representations,ost basic topics are touched on in this chapter. The more advanced theory of squareintegrable representations is given in the next chapter. A good reference for this chapter is Chapter 3 of the book [27] by Folland. A more comprehensive treatise is the book [55] by Kirillov.
发表于 2025-3-22 13:18:24 | 显示全部楼层
Unitary Representations,ost basic topics are touched on in this chapter. The more advanced theory of squareintegrable representations is given in the next chapter. A good reference for this chapter is Chapter 3 of the book [27] by Folland. A more comprehensive treatise is the book [55] by Kirillov.
发表于 2025-3-22 20:58:24 | 显示全部楼层
Wavelet Transforms,his book. It is in fact the wavelet transform associated to the admissible wavelet yo for the irreducible and square-integrable representation π: . → . of a locally compact and Hausdorff group . on a Hilbert space. To be more precise, we introduce the following definition.
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发表于 2025-3-23 05:11:26 | 显示全部楼层
A Sampling Theorem,resentation is a reproducing kernel Hilbert space, we give in this chapter a sampling theorem on a locally compact and Hausdorff group. This is an analogue of Shannon’s sampling theorem given in Section 2.4 of the book [7] by Blatter and Section 2.1 of the book [13] by Daubechies among others. The o
发表于 2025-3-23 08:21:11 | 显示全部楼层
A Sampling Theorem,resentation is a reproducing kernel Hilbert space, we give in this chapter a sampling theorem on a locally compact and Hausdorff group. This is an analogue of Shannon’s sampling theorem given in Section 2.4 of the book [7] by Blatter and Section 2.1 of the book [13] by Daubechies among others. The o
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