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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

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Gelfand representation and functional calculus applications beyond Functional Analysis

There are some examples in ergodic theory. Furstenberg's correspondence principle basically relays on Gelfand's representations. Another example - the functional calculus gives a very easy proof of …
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3 votes

Diophantine equations and ergodic theorems

It is a whole line of ideas (and proofs) which go usually by the name of ``Linnik's problems''. Apart from Linnik's book (and the Linnik-Skubenko theorem), it has been extensively studied by many rese …
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