As we were studying the modified wave equation A f = L f, where L is the Hodge Laplacian and Af = f'' +f'/t -f/t^2 is a a second Order Sturm Liouville Operator, I thought it would be interesting to solve Af = g using power series, something which has come up in Analysis II (which I took as a sophomore, a course taught by Eugene Trubowitz). If g has a convergent power series, then there exists a unique f with that property such that Af=g. This is a bit strange at first that a second order differential equation has a unique solution but the boundary condition f(0)=0 is forced by the set-up and the second boundary condition is having a bounded solution, which forces the initial velocity.
Happy piday.
