ADDENDUM: I want to point out I deleted the MathOverflow question. Apparently, someone on the site became concerned that it wasn't a good question for that site, and he mentioned how it wasn't good to post things that were too speculative, and since I noticed some problems, like the question of the convergence of the integrals is not sure, that still indicate more work needs to be done. Good luck with the paper, though. I suspect the ideas will be more complete, then. I just didn't want to harm that site any. He said that they had even gotten some false questions on this topic, and I could understand why he'd not be too happy about that. Hope you understand. Not to say this is false, but I got what he was driving at.
I hope you can understand.
I hope you can understand.