The beginning of section 12, Calculus of variations (chapter 3, Variational principles) in V. I. Arnold's Mathematical Methods of Classical Mechanics (2nd edition, p. 55) reads:

For what follows, we will need some facts from the calculus of variations. A more detailed exposition can be found in (...), or G. E. Shilov, "Elementary Functional Analysis," MIT Press, 1974.

However, Shilov's book (at least the 1996 Dover print) doesn't seem to be about the calculus of variations at all. Does anyone know what's going on here?

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    $\begingroup$ Some results of functional analysis can also be seen as facts of calculus of variations, so I am not sure if there is a real question here... $\endgroup$ – Sergio Parreiras Jul 25 '14 at 17:18
  • $\begingroup$ I browsed Shilov's book and didn't find anything relevant to the calculus of variations. If you can find something, I will accept it as an answer. $\endgroup$ – Ricardo Buring Jul 25 '14 at 17:39
  • $\begingroup$ I don't have Arnold nor Shilov books with me but does Arnold tells you explicitly which facts of calculus of variations he is assuming? $\endgroup$ – Sergio Parreiras Jul 25 '14 at 17:42

Yes, the reference is not correct.

The correct reference (which can be found in the original Russian edition) is to Shilov's Mathematical Analysis: Special Course.


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