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In mathematics, in the area of wavelet analysis, a refinable function is a function which fulfils some kind of self-similarity. A function is called refinable with respect to the mask if : This condition is called refinement equation, dilation equation or two-scale equation. Using the convolution (denoted by a star, *) of a function with a discrete mask and the dilation operator one can write more concisely: : It means that one obtains the function, again, if you convolve the function with a discrete mask and then scale it back. There is a similarity to iterated function systems and de Rham curves. The operator is linear. A refinable function is an eigenfunction of that operator. Its absolute value is not uniquely defined. That is, if is a refinable function, then for every the function is refinable, too. These functions play a fundamental role in wavelet theory as scaling functions. ==Properties== 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「refinable function」の詳細全文を読む スポンサード リンク
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