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| {{unreferenced |date= October 2010}}
| | Hi there, I am Alyson Boon even though it is not the name on my beginning certification. Alaska is the only location I've been residing in but now I'm considering other options. Office supervising is what she does for a residing. She is truly fond of caving but she doesn't have the time recently.<br><br>My weblog ... [http://netwk.hannam.ac.kr/xe/data_2/85669 email psychic readings] |
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| In [[mathematics]], the '''scale convolution''' of two [[Function (mathematics)|functions]] <math>s(t)</math> and <math>r(t)</math>, also known as their '''logarithmic convolution''' is defined as the function<br>dodo
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| :<math> s *_l r(t) = r *_l s(t) = \int_0^\infty s\left(\frac{t}{a}\right)r(a) \, \frac{da}{a}</math>
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| when this quantity exists.
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| ==Results==
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| The logarithmic convolution can be related to the ordinary [[convolution]] by changing the [[Variable (mathematics)|variable]] from <math>t</math> to <math>v = \log t</math>:
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| : <math> s *_l r(t) = \int_0^\infty s\left(\frac{t}{a}\right)r(a) \, \frac{da}{a} =
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| \int_{-\infty}^\infty s\left(\frac{t}{e^u}\right) r(e^u) \, du </math>
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| :<math> = \int_{-\infty}^\infty s\left(e^{\log t - u}\right)r(e^u) \, du.</math>
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| Define <math>f(v) = s(e^v)</math> and <math>g(v) = r(e^v)</math> and let <math>v = \log t</math>, then
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| :<math> s *_l r(v) = f * g(v) = g * f(v) = r *_l s(v).\, </math>
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| {{PlanetMath attribution|id=5995|title=logarithmic convolution}}
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| [[Category:Logarithms]]
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Revision as of 23:23, 8 February 2014
Hi there, I am Alyson Boon even though it is not the name on my beginning certification. Alaska is the only location I've been residing in but now I'm considering other options. Office supervising is what she does for a residing. She is truly fond of caving but she doesn't have the time recently.
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