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In mathematics, a Green's function is the impulse response of an inhomogeneous linear differential operator defined on a domain with specified initial conditions or boundary conditions. This means that if L is the linear differential operator, then * the Green's function G is the solution of the equation LG = δ, where δ is Dirac's delta function; * the solution of the initial-value problem Ly = f is the convolution (G ⁎ f), where G is the Green's function.

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