A Periodic Faddeev-Type Solution Operator

We construct periodic solution operators for the equationΔu+2iζ• u=fin a bounded domain with the help of Fourier series. We prove that theL2-norms of these operators converge to zero if the parameter Im ζ goes to infinity. Then we apply these operators to show that functionsu C20(Rd) satisfying an inequality Δu(x) M u(x) inRdmust vanish everywhere. We extend this result to other second order elliptic differential operators with constant coefficients replacing the Laplacian. Finally, we use the solution operators to derive that the span of products of solutions to differential equations is dense inL1.