Let n E N and f : R" - R such that f is a radial (spherical symmetry) functions, i.e. Vo,y e R" with |x]) = ly| = (vy; + ..+>?) one has f(z) = f(y). (a) Compute Af(x) = 02 f + .. + 02 f in terms of the variable r = (vc? + .. + x2). (b) Given f, g : R3 - R radial functions with f(r) = F(x]) and g(c) = G(|x]), where F, G : R - R are even, find the solution of the IVP OFw - Aw =0, CER, tER w(x, 0) = f(x) = F(|:[), atw(x, 0) = g(x) = G(|=))