The k-th derivative of this function is negative one to the k times the k-th derivative of test functions phi evaluated at zero. For a non-zero scalar alpha, this function of alpha-x equals this function of x divided by the magnitude of alpha. The convolution of this function with any other tempered distribution S is S since its Fourier transform is 1. Applying an operator to its associated (*) Green’s function gives this distribution. (10[1])This distribution’s sifting property integrates over all space and will return another function’s evaluation where this distribution is centered. This distribution is the derivative of the Heaviside step function and is the limit of a Gaussian as it gets taller and thinner. (10[1])For 10 points, name this distribution which is zero everywhere except at the origin, where it is infinite. ■END■