Is there an obvious link between Analysis and Group theory?

Question

For instance, Number theory can be seen as a subfield of Analysis, and Linear algebra is indeed definitely a subfield of Group theory - and both might in fact be generalised under some area of studies between Set theory and Group theory that I have not come across yet.

The question is, is there such a field that contains Analysis and Group theory as subfields? Or in other words, is there an obvious link between Analysis and Group theory?

Answer 1

Aside from the fact that "analysis" and "group theory" are different classification levels (like "plants" and "vertebrates" in biology), all things related to Lie Groups form a significant mix of analysis and group theory.

Answer 2

There is something called Topological Groups which can carry (the locally compact ones) a Haar measure, comparable to Riemann or Lebesgue. You can “do analysis” with these kinds of groups.