What is convolution, how does it relate to inner product? My final question is: what is the intuition behind convolution? what is its relation with the inner product? I would appreciate it if you include the examples I gave above and correct me if I am wrong
Proving commutativity of convolution $ (f \ast g) (x) = (g \ast f) (x)$ But we can still find valid Laplace transforms of f (t) = t and g (t) = (t^2) If we multiply their Laplace transforms, and then inverse Laplace transform the result, shouldn't the result be a convolution of f and g?
analysis - History of convolution - Mathematics Stack Exchange It the operation convolution (I think) in analysis (perhaps, in other branch of mathematics as well) is like one of the most useful operation (perhaps after the four fundamental operations addition, subtraction, multiplication, division) MY Question: How old the operation convolution is? In other words, the idea of convolution goes back to whom?
real analysis - Convolution of two gaussian functions - Mathematics . . . You should end up with a new gaussian : take the Fourier tranform of the convolution to get the product of two new gaussians (as the Fourier transform of a gaussian is still a gaussian), then take the inverse Fourier transform to get another gaussian