I want to know the answer to the following question:
What variables do locally compact groups share that can be studied by harmonic analysis?
All the background I'm provided with is that "In order for the group law and the topology to interweave well, the group operations must be continuous functions, that is, g • h, and g−1 must not vary wildly if g and h vary only little.". Is that enough to answer the question?
Answer: no