ChapterZero

I’ve been at TAMU for a week now; actually, I’m at home right now, because I had to come pick up my check, order new eye-glasses, and get more clothes. This is my first posting since I’ve been there, because my mom was having what she thought was an issue with my hosters, so she had stopped paying the bill.

My schedule is very open: we have classes on MWF from 12pm-2:40pm– that is the only assigned activity we have (where we is the people in the wavelets research group; the other groups have more imposed scheduling structures). During the rest of the time, we do whatever; actually, there is a lot of homework to do, which takes a significant amount of time. So far, we’ve talked about inner product and normed spaces, orthonormal systems, and basic frame theory. Last class, we were introduced to some operator theory associated with frame theory– pretty interesting stuff, but I’m stuck on the frame theory stuff. Some things that seem to be pretty straight-forward, at least to Keri (the grad. student lecturing us on frame theory), are not at all clear to me. For instance, why is it that a frame satisfies the reconstruction theorem if and only if it is a tight frame? On a related note, why is a tight frame in a finite-dimensional Hilbert space necessarily an orthonormal system? Analytically, my problem is manipulating inner products when the vectors being dealt with are not orthonormal. Conceptually– and there must be a problem here, as it informs all analytic manipulations–, I don’t think I have a firm grasp of the frame concept.

To that end, while I’m at UH picking up my paycheck, I’m going to raid the library for books on frame theory, operator theory, and wavelets. I doubt I’ll read them all, or even significant portions of any of them, but I would like to have them just in case. I would rather not have to carry so many books with me, but TAMU only lets visitors check out 5 at a time.