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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 Fourier inversion theorem ： ウィキペディア英語版 Fourier inversion theorem In mathematics, the Fourier inversion theorem says that for many types of functions it is possible to recover a function from its Fourier transform. Intuitively it may be viewed as the statement that if we know all frequency and phase information about a wave then we may reconstruct the original wave precisely. The theorem says that if we have a function $f:\backslash mathbb\backslash rightarrow\; \backslash mathbb$ satisfying certain conditions, and we use the convention for the Fourier transform that :$(\backslash mathcalf)(\backslash xi):=\backslash int\_\; e^\; \backslash ,\; f(y)\backslash ,dy,$ then :$f(x)=\backslash int\_\; e^\; \backslash ,\; (\backslash mathcalf)(\backslash xi)\backslash ,d\backslash xi.$ In other words, the theorem says that :$f(x)=\backslash int\_\; \backslash int\_\; e^\; \backslash ,\; f(y)\backslash ,dy\backslash ,d\backslash xi.$ This last equation is called the Fourier integral theorem. Another way to state the theorem is to note that if is the flip operator i.e. , then :$\backslash mathcal^=\backslash mathcalR=R\backslash mathcal.$ The theorem holds if both and its Fourier transform are absolutely integrable (in the Lebesgue sense) and is continuous at the point . However, even under more general conditions versions of the Fourier inversion theorem hold. In these cases the integrals above may not make sense, or the theorem may hold for almost all rather than for all . ==Statement== In this section we assume that is an integrable continuous function. Use the convention for the Fourier transform that :$(\backslash mathcalf)(\backslash xi):=\backslash int\_\; e^\; \backslash ,\; f(y)\backslash ,dy.$ Furthermore, we assume that the Fourier transform is also integrable. 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「Fourier inversion theorem」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.