Definition talk:Differentiable Functional

I don't know if the book in question gives one, but would you mind figuring out a formal definition? It seems like you'd need to do something like replace the $\epsilon$ by a function and requiring that it tends to zero with $h$, or something. Depends on what $\Delta$ means.

Also: is the convergence $\epsilon\to0$ uniform in $y$? I guess not, because that would be strong. Locally uniform maybe? --barto (talk) 14:53, 30 April 2017 (EDT)

Compare with the definition of differentiablilty in Banach spaces. --barto (talk) 14:56, 30 April 2017 (EDT)


 * The author of these pages has previously communicated that he is not prepared to put them into any semblance of order or conformity, as he is of the opinion (not shared by all editors) that such things are of negligible importance compared with the actual placing of this material online.


 * I have the Gelfand and Fomin work on my own shelf, so (once I've finished enjoying myself with these entertaining little morsels of recreational mathematics) I may take some time to go through this series of results myself and do the necessary work, but until then we may find it best to watch this category from a distance, so to speak. --prime mover (talk) 15:09, 30 April 2017 (EDT)


 * Ok, no problem. --barto (talk) 15:18, 30 April 2017 (EDT)