One last thing: I find it kind of funny that for the whole week, I've been doing harmonic analysis and didn't even know it!! Apparently a functional analytic/measure theoretic study of harmonic functions is considered harmonic analysis :).

Also, I'm totally stuck on one of the Rudin problems: finding conditions where one invariant subspace of the shift is propery contained in another. I'll try tommorow again.

So today I got through quite an elegent result in math: Beurling's theorem. It completely characterizes the invariant subspace of the unilaterial shift on l_2. The idea is to switch from l_2 to H^2 (the Hardy space) and so using Hardy space theory, these subspaces are completely determined by (and to each combination one can associate an ( Read more... )

God do I love my friends :) (nilsan isn't the person's full nickname on AIM ( Read more... )

This just made my day. :)


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You know, I have to admit that the complex analysis I'm studying (Hardy Space/Bergman Space theory) is absolutely amazing. It's a beautiful combination of functional analysis (basic hilbert/banach space theory, basic function spaces and their duals, etc), measure theory (borel measures on the unit circle, differentiation of complex measures, etc ( Read more... )

I remember watching Black Hawk Down (one of my fav movies) and listening to some of its music. A portion of the music had a VERY distinct sound similar to old Dead Can Dance, and well what do you know, turns out Lisa Gerrard (of DCD fame) did some of the music.

I think actually, the direct sum of a shift and a unitary operator is another shift plus a rank-one operator (which is of course compact.) Of course it's almost trivial to prove this it seems. I'll recheck it tommorow ( Read more... )

Anyway I'm going to ramble about how I'm pissed that Uni of Pitts didn't give me support. HOW THE FUCK DID THIS HAPPEN!!! After reading my paper, one of the professors (chris lennard )literally solicited me to be his advisee. Yet I was put on the shortlist, and apparently not high up on the list. Meh ( Read more... )

So, for the last three days we (SUNY Buffalo) have had one hour talks by Bill Arveson. Two of them are on the utterly bizzare intersection of operator theory and algebraic geometry/commutative algebra. Needless to say, I understood nothing lol ( Read more... )