The only thing that jumped out at me as the difference between the one on your profile and a google image search was the lack of 'tail', for want of a better word, on the 'a' but as Ellie said, a handwriting expert would probably give you a better answer
I have googled and it does look similar - its the way the J and the H are joined, and the looping and short stick (or whatever the upright bit is called) on the l and d. I think 1939 was quite early in his career wasn't it? And it does seem to look more like the earlier ones I can find.
I don't have the spare cash to get a professional opinion, hence asking on AIBU
My guess would be that it's genuine. There's a big difference between signing something and writing your name - but the overall handwriting does seem to be very similar in all the examples. Also, seems an odd thing for a faker to do - sign a book that (I think) isn't known for having any connection to him. I think a faker would sign the novel Psycho. Or would that be too obvious?