I've reading a little bit about applied functional analysis and get a lot of information about its relation with existence and uniqueness of solutions of equations, for instance, equivalence of equations, etc.
However, I do not find yet a direction about the following question: It seems to me that today all the results of FAnalysis that are applied are "already done" or about PDE/ODE's. I mean, the theorical results about spaces, etc., are they applied today? Seems the modern research in FAnalysis is applied only on PDE/ODE's. Is it true?
I mean, there is some subject of research that uses, today, theorical FAnalysis and applied math? Particularly interested on biomathemathics, oxigenation, or something similar.
Many thanks in advance!