Solving strange equations

How does one go about solving strange equations like:

 \phi(t) = \sum_k c_k \phi(2t - k)

where all you know is \{c_k\}_k\in\Z is square summable? How would you find \phi that satisfies this, and is there more than one?

It’s an interesting question to consider. I know the answer, but I can’t imagine how I’d work it out if I hadn’t seen someone else work it out.

Leave a Reply