Green's function

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In mathematics, a Green's function (or Green 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 {\displaystyle L} is a linear differential operator, then the Green's function G {\displaystyle G} is the solution of the equation L G = δ , {\displaystyle LG=\delta ,} where δ {\displaystyle \delta } is Dirac's delta function; the solution of the inhomogeneous problem L y = f {\displaystyle Ly=f} is the convolution, y = ( G ∗ f ) . {\displaystyle y=(G\ast f).} By the superposition principle, given...

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