Jim,
If removal of the trees is a desirable thing for you,
and you're not opposed to limited, targeted herbicide
application, cutting down &/or girdling the trees and
concurrent application of an appropriate herbicide
labeled for stump treatment, like Brush-B-Gon,
Pathway(Tordon), Garlon, etc., will quite effectively
kill those trees, and ultimately, their roots.
I use Pathway on undesirable tree species, like
sweetgum, honeylocust, and black locust when it's in
an undesirable location. Total kill with no stump or
root sprouting.