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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
1
vote
Accepted
Why are we interested in operators that share a basis of eigenfunctions?
I'm not sure what precisely you are looking for but let me try the guess an answer on the soft end (basic intuition stuff) of what you are asking. I'm not qualified for the hard end of this question, …
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Accepted
Reference request: Expository paper on the use of functional analysis in differential and in...
The following source has a number of chapters devoted to applications of functional analysis to differential and integral equations:
Paul Sacks "Techniques of functional analysis for differential and …