235 reputation
29
bio website
location University of California, San Diego
age 24
visits member for 1 year, 5 months
seen 5 hours ago
I am a graduate student at University of California, San Diego under the advice of Jim Agler.

Aug
19
comment Is there an algebraic number that cannot be expressed using only elementary functions?
In your post on stackexchange you allowed $i,$ and other elemenary complex analysis: do you still want to do this? It seems if you include integration, it would be possible to express any algebraic number this way. Anyway for an algebraic number $a$ with minimum polynomial $p,$ $a = \int_{\gamma} \frac{zp'(z)}{p(z)} dz,$ where $\gamma$ is a circle with rational radius and center, containing $a$ and no other roots of $p.$
Aug
7
comment Invertibility of random Vandermonde matrix
Yeah, you definitely need to use non-atomicity. I think you need something a bit stronger, since if the points lie in certain varieties, you may run into trouble.
Aug
7
answered Invertibility of random Vandermonde matrix
Aug
4
comment What summations of elementary trig functions are known to have (elementary) closed forms?
If you mean $\Sigma^{\infty}_{k=0} \tan{k},$ I think that sum does not converge. Can you be more explicit about what sums you're talking about?
Aug
3
comment largest eigenvalue of a symmetric matrix
I mean $I$ to be the N by N identity matrix.
Aug
3
comment largest eigenvalue of a symmetric matrix
Then it would seem that taking $\Phi = -I$ and $P = I,$ where I, would imply that the phenomenon is indeed a coincidence. Although, with some extra special structure, the phenomenon may hold.
Aug
3
comment largest eigenvalue of a symmetric matrix
What is $\Phi?$
Jul
31
awarded  Enlightened
Jul
31
awarded  Nice Answer
Jul
31
awarded  Yearling
Jul
30
comment Prove that …, f(x-2), f(x-1), f(x), f(x+1), f(x+2),… is algebraically linearly independent without the Fourier transform
$\cos x$ isn't in $L^2.$
Jul
30
awarded  Critic
Jul
29
revised Homogenous polynomially convex hull of $[0,1]^n$
grammatical fix
Jul
29
asked Homogenous polynomially convex hull of $[0,1]^n$
Jul
29
comment Prove that …, f(x-2), f(x-1), f(x), f(x+1), f(x+2),… is algebraically linearly independent without the Fourier transform
I guess the simplest answer would be that the function $\|v\|_S = (\sum_{k\in S} \langle v,f(x-k) \rangle^{2})^{1/2}$ defines a norm on $V$ which is finite dimensional, and all norms on a finite dimensional space are equivalent in the sense that they induce the same topology.
Jul
29
comment Prove that …, f(x-2), f(x-1), f(x), f(x+1), f(x+2),… is algebraically linearly independent without the Fourier transform
Sorry, I meant to write $f(x-m).$
Jul
29
comment Prove that …, f(x-2), f(x-1), f(x), f(x+1), f(x+2),… is algebraically linearly independent without the Fourier transform
Bartgol, he's talking about the functions $f(x-k) \in L^2,$ not the values of $f$ at the integers which wouldn't be well defined anyway.
Jul
29
comment Prove that …, f(x-2), f(x-1), f(x), f(x+1), f(x+2),… is algebraically linearly independent without the Fourier transform
Well suppose you had a linear dependence, i.e. there $\sum^n_{k=-l} a_kf(x-k) =0,$ where $a_{-l}$ and $a_n$ are non-zero. By applying the shift, we get that $\sum^n_{k=-l} a_kf(x-(k+t)) =0.$ That is, for any $m > n$ or $m< -l$ we can write $f(m)$ in terms of a recurrence relation.
Jul
29
answered Prove that …, f(x-2), f(x-1), f(x), f(x+1), f(x+2),… is algebraically linearly independent without the Fourier transform
Jan
11
awarded  Teacher