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In mathematics, an integral transform is any transform ''T'' of the following form: : The input of this transform is a function ''f'', and the output is another function ''Tf''. An integral transform is a particular kind of mathematical operator. There are numerous useful integral transforms. Each is specified by a choice of the function ''K'' of two variables, the kernel function or nucleus of the transform. Some kernels have an associated ''inverse kernel'' ''K''−1(''u, t'') which (roughly speaking) yields an inverse transform: : A ''symmetric kernel'' is one that is unchanged when the two variables are permuted. == Motivation == Mathematical notation aside, the motivation behind integral transforms is easy to understand. There are many classes of problems that are difficult to solve—or at least quite unwieldy algebraically—in their original representations. An integral transform "maps" an equation from its original "domain" into another domain. Manipulating and solving the equation in the target domain can be much easier than manipulation and solution in the original domain. The solution is then mapped back to the original domain with the inverse of the integral transform. Also there are many applications of probability that rely on integral transforms, such as "pricing kernel" or stochastic discount factor, or the smoothing of data recovered from robust statistics, see kernel (statistics). 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「Integral transform」の詳細全文を読む スポンサード リンク
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