Inverse Operator

  • Thread starter tpm
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  • #1
tpm
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Don't know if i'm wrong or this makes sense but if:

[tex] \frac{1}{D}f= \int dx f(x) [/tex]

Where D is the derivative operator and the integral is indefinite, my question is if as a generalization of this then:

[tex] \frac{1}{D_{x}+D_{y}}f= \iint dxdy f(x,y) [/tex]

(Double indefinite integral over x and y) and so on ....
 

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  • #2
matt grime
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Did you even try it on a few examples?
 
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  • #3
tpm
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I have tried this:

[tex] \frac{1}{D_{x}+D_{y})f=g [/tex]

then we can put it in the form:

[tex] \frac{\partial g}{\partial x}+\frac{\partial g}{\partial y}=f [/tex]

HOwever i don't know how to solve this PDE to get 'f'
 

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