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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク FBI transform ： ウィキペディア英語版 FBI transform In mathematics, the FBI transform or Fourier–Bros–Iagolnitzer transform is a generalization of the Fourier transform developed by the French mathematical physicists Jacques Bros and Daniel Iagolnitzer in order to characterise the local analyticity of functions (or distributions) on R''n''. The transform provides an alternative approach to analytic wave front sets of distributions, developed independently by the Japanese mathematicians Mikio Sato, Masaki Kashiwara and Takahiro Kawai in their approach to microlocal analysis. It can also be used to prove the analyticity of solutions of analytic elliptic partial differential equations as well as a version of the classical uniqueness theorem, strengthening the Cauchy–Kowalevski theorem, due to the Swedish mathematician Erik Holmgren (1873–1943). ==Definitions== The Fourier transform of a Schwartz function ''f'' in ''S''(R''n'') is defined by :$(f)(t)\; =\; (2\backslash pi)^\; \backslash int\_^n\}f(x)\; e^\backslash ,\; dx.$ The FBI transform of ''f'' is defined for ''a'' ≥ 0 by :$(\_a\; f)(t,y)\; =\; (2\backslash pi)^\; \backslash int\_^n\}f(x)e^\; e^\backslash ,\; dx.$ Thus, when ''a'' = 0, it essentially coincides with the Fourier transform. The same formulas can be used to define the Fourier and FBI transforms of tempered distributions in ''S(R''n''). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「FBI transform」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.