I've fallen into heavier math than I'm prepared for, would love to hear from someone who knows about linear operators. The impetus is work by
Lars Hansen and coauthors that (i) expresses asset pricing as a linear operator and (ii) applies Perron-Frobenius-like methods to derive long-horizon returns. This is well-known in bond pricing circles, where many models have the feature that yields on long bonds converge. We -- meaning Stan Zin and Mike Chernov -- have a summary
here of Hansen's work here [see eq (10) and the surrounding discussion].
Hansen's idea is to focus on the dominant eigenvalue and associated eigenvector/eigenfunction, but we've be thinking it might be useful to look at all of them and see where that leads. We're now surrounded by books on functional analysis, but it's been slow going. If this is something that interests you, please get in touch.