Difference between revisions of "Convolution"
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− | + | The '''convolution''' of two functions can mean various things. | |
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− | + | In [[number theory | number theoretic]] context, convolution of two functions <math> f,g : \mathbb{N} \rightarrow \mathbb{C} </math> usually means [[Dirichlet convolution]], defined as <math> \displaystyle f * g = \sum_{d\mid n} f(d)g\left( \frac{n}{d} \right) </math>. | |
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− | + | In [[analysis | analytic]] context, convolution of functions <math> \displaystyle f, g </math> usually means a function of the form <math> \int f(\tau) g(t-\tau) d\tau </math>. | |
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Latest revision as of 19:12, 7 June 2007
The convolution of two functions can mean various things.
In number theoretic context, convolution of two functions usually means Dirichlet convolution, defined as
.
In analytic context, convolution of functions usually means a function of the form
.
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