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^{1}f(x,t,H(x-t)*a)dt), where a is a constant, H(x) is the Heaviside step function, and f is

I know it must have something to do with distributions and the derivative of the Heaviside function which is ∂/∂t(H(t))=δ(x)... but I don't understand how can I work with the Heaviside function being an argument of the function...