If there is unquestionable evidence that has been checked and double checked and there is no other way that it can't have been that person and the evidence has been thoroughly checked for anything that is fake evidence as well and the person is definately the person who done it, then yes they should be on death row. BUT, I beleive that before they are put to death they should be given a certain number of years. This not only punishes them while they're alive but it also gives time for the evidence to be checked etc.
I once heard of a guy who was convicted of a mass murder. He was put to death within 6 months. A short time after, it turned out it was not him.