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Logarithmic convolution : ウィキペディア英語版
Logarithmic convolution

In mathematics, the scale convolution of two functions s(t) and r(t), also known as their logarithmic convolution is defined as the function
dodo
: s
*_l r(t) = r
*_l s(t) = \int_0^\infty s\left(\frac\right)r(a) \, \frac
when this quantity exists.
==Results==
The logarithmic convolution can be related to the ordinary convolution by changing the variable from t to v = \log t:
: s
*_l r(t) = \int_0^\infty s\left(\frac\right)r(a) \, \frac =
\int_^\infty s\left(\frac\right) r(e^u) \, du
: = \int_^\infty s\left(e^\right)r(e^u) \, du.
Define f(v) = s(e^v) and g(v) = r(e^v) and let v = \log t, then
: s
*_l r(v) = f
* g(v) = g
* f(v) = r
*_l s(v).\,

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「Logarithmic convolution」の詳細全文を読む



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