The e-book would contain a special autograph page, or the device itself would allow the page to be generated on the fly by the author. Using a special app such as iBooks Author, the author would send an autograph to the page via Bluetooth or another wireless technology. The author and the receiving device would naturally have to be near each other for all of this to work.
A certificate would be transferred as proof that the autograph is authentic.
There's no way this is going to catch on. It's too complicated, and it's not the same thing as an autograph. Tech companies have been trying to resolve this issue of autographing e-books for a decade now, and none of the solutions have stuck. People still want autographs. I've seen plenty of people at readings asking authors to autograph the backs of e-readers. Which makes sense, because that means something. The author was there, and the author signed their name to an item of importance. Files serve many great important purposes, but it's impossible to get sentimental about a file in the same way you do about a book, because the file doesn't have a physical existence. The only way to "solve" this e-book autographing "problem" is to create a physical version of the e-book and have the author sign it. Which would be a book. And then you're right back at the beginning.