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convolution

Norman Albers
in Analysis and Calculus

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I am trying to calculate a convolution integral in Fourier transform, and still struggling with my fear of convolution. In the inhomogneous field of my photon model the source term of current involves [math][-\lambda^2 + a^2(y^2 + z^2)]A[/math] , where the vector potential was constructed as a Gaussian wave packet of cylindric symmetry. I'd welcome comments to help me see my way clear here; these expressions in k-space can be awkward. Is there an easy generalizable statement, given that I have written the transform of [math] A_y= A_o cos(kX-\omega t)e^{-a^2(X^2+y^2+z^2)}[/math]?

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I solved the problem by integration by parts, and so am still beset by the fear of convolution. You may read over in "open question on QM".

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