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Copy file name to clipboardExpand all lines: docs/src/usage/operators.md
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@@ -6,7 +6,7 @@ using ApproxFun, LinearAlgebra
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Linear operators between two spaces in ApproxFun are represented by subtypes of `Operator`. Every operator has a `domainspace` and `rangespace`. That is, if a `Fun``f` has the space `domainspace(op)`, then`op*f` is a `Fun` with space `rangespace(op)`.
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Note that the size of an operator is specified by the dimension of the domain and range space.
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Note that the size of an operator is specified by the dimension of the domain and range space.
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## Calculus operators
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D + C
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```
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ApproxFun can automatically determine the spaces, so if one writes `D + I` it will translate it to `D + C`.
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ApproxFun can automatically determine the spaces, so if one writes `D + I` it will translate it to `D + C`.
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Now consider the Fredholm integral operator of the second kind:
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f = Fun(cos,Fourier()); (π*f)(0.1)
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```
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Behind the scenes, `Derivative()` is equivalent to `Derivative(UnsetSpace(),1)`. When multiplying a function `f`, the domain space is promoted before multiplying, that is, `Derivative()*f` is equivalent to `Derivative(space(f))*f`.
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Behind the scenes, `Derivative()` is equivalent to `Derivative(UnsetSpace(),1)`. When multiplying a function `f`, the domain space is promoted before multiplying, that is, `Derivative()*f` is equivalent to `Derivative(space(f))*f`.
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This promotion of the domain space happens even when operators have spaces attached. This facilitates the following construction:
Note that `rangespace(D) β Β Chebyshev()`, hence the operators are not compatible. Therefore, it has thrown away its domain space, and thus this is equivalent to `Derivative(rangespace(D))*D`.
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