Recent content by l'Hôpital

Hey, I've actually been here for a while, I'm just...uh...I guess inactive lately haha. I've been here through all parts of my math career, even since I was a freshman in college! I really like these ideas for programming. Currently, I plan on taking this intense course on Python in two weeks...

Hey guys! Let me throw in who I am before I introduce my question. I finished my year of graduate school last May, figured out an advisor and a field (something related with Brownian motion on manifolds), and I'm overall happy with it all. No plans of dropping out, I enjoy the company of my...

Nevermind, got it! Thanks anyways!

Ooh! I like it! Awesome, thanks! One more question: They also makes a claim as follows. Let P : L^2 \rightarrow V_{n} be the projection operator. Then, it can be represented as an integral operator with kernel K(x,y) = l\sum_{i=1}^{l} 1_{A_i} (x) 1_{A_i} (y) where \cup A_i = X are...

Context: T : X \rightarrow X is a measure preserving ergodic transformation of a probability measure space X. Let V_n = \{ g | g \circ T^n = g \} and E = span [ \{g | g \circ T = \lambda g, for some \lambda \} ] be the span of the eigenfunctions of the induced operator T : L^2 \rightarrow...

Alright. So, by the integral condition and the residue theorem (in that order), we get the equalities 0 = \int zf^2 dz = Res(zf^2,0) Since we are assuming it's a simple pole of f, it's an order 2 pole of f^2, hence simple pole of zf^2, so the residue boils down to the limit condition \lim_{z...

Oh wow. Shameful. Shameful, shameful, shameful. Been doing too much real stuff lately haha. How about this? By the integral condition, it suffices to only consider f having simple poles as discontinuities. Wlog, we assume it has a pole at z = 0 and choose a contour around it which only has...

Homework Statement http://www.math.northwestern.edu/graduate/prelims/AnalysisPrelim2010FallFinalVersion.pdf Problem 2 of Part III. Homework Equations Complex Analysis. The Attempt at a Solution So, I think my proof is wrong (since I never used the fact that it was f^2) as opposed to f...

This sort of came up the other day: Given a sequence of monotonically decreasing points, a_n, such that a_n \rightarrow 0 does there exist an analytic f on ℝ such that f(n) = a_n ? I figured there should be some sort interpolation theory on this, but I haven't found anything...

I dunno. I sort of freaked out for the first section, and actually eve nran out of time. Then the next two sections I did went fine, just...I don't know. It's scary.

Hey all, So I took the General GRE, and I did rather poorly in the GRE Quant score (161). However, most of my resume and the likes would point otherwise (typical stuff like graduate coursework, two REUs, 3.9 GPA, etc.) How concerned should I be about this? Should I retake it? I'm taking...

http://en.wikipedia.org/wiki/Infinite_product#Product_representations_of_functions Look at the one for sine. What happens if you plug in z = i?

So who all is attending SMALL this summer? In particular, the Ergodic Theory one?

@76: Thanks! Sorry to hear that. : (. Maybe next year? @Double: They said I have to make a decision by Thursday morning. I'll probably send an e-mail tonight or tomorrow. So yes, hopefully we'll see each other this summer!

Yes, I had a phone interview and we talked for a bit. I kinda psyched myself out, and probably sounded like an idiot haha. Such is life though. He also asked me if I had any questions and I said no, which was probably a bad idea too. EDIT: Wait no, I lied. Just got an offer from SMALL! Woot!