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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 Fredholm integral equation ： ウィキペディア英語版 Fredholm integral equation In mathematics, the Fredholm integral equation is an integral equation whose solution gives rise to Fredholm theory, the study of Fredholm kernels and Fredholm operators. The integral equation was studied by Ivar Fredholm. ==Equation of the first kind== Fredholm Equation is an Integral Equation in which the term containing the Kernel Function (defined below) has constants as integration limits. A closely related form is the Volterra integral equation which has variable integral limits. An inhomogeneous Fredholm equation of the first kind is written as: :$g(t)=\backslash int\_a^b\; K(t,s)f(s)\backslash ,\backslash mathrms$ and the problem is, given the continuous kernel function $K(t,s)$ and the function $g(t)$, to find the function $f(s)$. If the kernel is a function only of the difference of its arguments, namely $K(t,s)=K(t-s)$, and the limits of integration are $\backslash pm\; \backslash infty$, then the right hand side of the equation can be rewritten as a convolution of the functions ''K'' and ''f'' and therefore the solution will be given by :$f(t)\; =\; \backslash mathcal\_\backslash omega^\backslash left(\backslash omega)\}$ \right]=\int_^\infty _t()(\omega)}e^ \mathrm\omega where $\backslash mathcal\_t$ and $\backslash mathcal\_\backslash omega^$ are the direct and inverse Fourier transforms respectively. 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「Fredholm integral equation」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.