Master's Thesis

I know what the factor for in the definition of the Fourier transform

means, if that factor is seen as a function in : If is fixed, then the variation of delivers the circle function, returning to the starting point for every .

But what if ? Here, has to be understood as the inner product and the integral turns into the -dimensional Lebesgue-integral, i.e., if , this means

Now, what has to be understood by in higher dimensions?