Quote by Dick
Try exploiting your hunch that it looks like a second derivative operator. Then what should eigensequences look like?

Oh, I think I understand! This finite difference approximation has error of order h^3, so if the terms in my series are e^(kn) expanded to order n^2 I should have an eigensequence. But it seems like this sequence isn't square summable except of course for k = 0, because otherwise it will diverge at one end... so the point spectrum is just 0, and the rest of the real line is in the continuous spectrum?