Wavelets, vibrations, and scalings
著者
書誌事項
Wavelets, vibrations, and scalings
(CRM monograph series, v. 9)
American Mathematical Society, c1998
大学図書館所蔵 全45件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographical references and index
内容説明・目次
内容説明
Physicists and mathematicians are intensely studying fractal sets of fractal curves. Mandelbrot advocated modeling of real-life signals by fractal or multifractal functions. One example is fractional Brownian motion, where large-scale behavior is related to a corresponding infrared divergence. Self-similarities and scaling laws play a key role in this new area. There is a widely accepted belief that wavelet analysis should provide the best available tool to unveil such scaling laws. And orthonormal wavelet bases are the only existing bases which are structurally invariant through dyadic dilations.This book discusses the relevance of wavelet analysis to problems in which self-similarities are important. Among the conclusions drawn are the following: a weak form of self-similarity can be given a simple characterization through size estimates on wavelet coefficients, and wavelet bases can be tuned in order to provide a sharper characterization of this self-similarity. A pioneer of the wavelet 'saga', Meyer gives new and as yet unpublished results throughout the book. It is recommended to scientists wishing to apply wavelet analysis to multifractal signal processing.
目次
Introduction Scaling exponents at small scales Infrared divergences and Hadamard's finite parts The 2-microlocal spaces C^{s,s^{\prime}}_{x_0}$ New characterizations of the two-microlocal spaces An adapted wavelet basis Combining a Wilson basis with a wavelet basis Bibliography Index Greek symbols Roman symbols.
「Nielsen BookData」 より