I am having a difficulty with a convolution. I recently asked a question about something similar and received a very good response so I am hoping one of you kind folks will know what to do here:
$\int B'(x)S'(\xi)\log|x-\xi|d\xi $
and
$\int (xB(x))'S'(\xi)\log|x-\xi|d\xi $
I have a vector for each of the variables that depend on x shown above . I also know that I can use: $B'(x)*S(x)=\int B'(x)S(x)dx $
would it be true to say:
$B'(x)*S'(x)=\int B'(x)S'(x)dx $
and is there a way for accounting for the logarithm before I convolute the functions? I am using Matlab and the built in function (conv(u,v)) seems to work fine for two functions. I can use the derivative of one of them and convolute the result with the second function, but I am unsure if the result will be valid if I differentiate both functions. I also don't know where the logarithm comes in. Any help or suggestions would be greatly appreciated.