Not sure if it helps, but the signature probably dates to around 1940-1943. My great-grandfather owned a diner in Hoboken at the time, which Sinatra used to frequent. He was the "Tex" to whom the signer addressed the autograph. I do not know anything as to the exact origin of this specific photo, but I'm hoping it's legit.
My initial observation is that it is Sinatra's signature. I like the characteristics in the writin style plus he references something personal about the food which helps. The condition looks a little rough. Are thinking of selling it?
Joe, thanks so much for the feedback. The photo itself is a little rough, but then again I'm sure it was not too well taken care of over the first 40 years of its existence. I will probably hold onto it because I am a Sinatra fan and it was handed down through my family. I would just like the peace-of-mind knowing its legit. Here's another one that is made out to my grandfather (from I'm assuming the same era) but I see some differences compared to the other one. What are your thoughts on this one?