what math branch deals with functional space where composition of the functions are operations?

Question

what is the math branch that research functional space where composition of the functions are operations?

Hilbert space and other linear functional space mainly research on the addition and scalar multiplication of two functions in the space. such as if f1 + f2 , and a*f,

what if compositions of functions are allowed inside the space? such as f1(f2). ?

Is there a particular math branch that research this space? maybe a sub-branch of functional analysis?

If addition and scalar multiplication are considered, it's because they lead to vector spaces, which have many desirable properties. Composition is not linear in general. The closest I see to what you want would be operator theory. — Jean-Claude Arbaut, Jun 02 '18 at 12:52
Looks like operator theory also considers linear functional space mostly, maybe nonlinear functional analysis? — martingale, Jun 02 '18 at 13:03
Try taking a look at this: https://www.springer.com/us/book/9783319168975 — , Jun 02 '18 at 14:30
Thanks. ergodic theory? is that the same as ergodic theory in random process — martingale, Jun 03 '18 at 01:22

score 0 · Answer 1 · answered Jun 05 '18 at 00:48

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I asked around and found that Groupoid might be a good model for this, and question is what Groupoid only deals with composition?

answered Jun 05 '18 at 00:48

martingale

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what math branch deals with functional space where composition of the functions are operations?

1 Answers1