2,286 reputation
11427
bio website math.princeton.edu/directory/…
location Princeton, New Jersey
age 26
visits member for 4 years, 8 months
seen 51 mins ago

PhD student at Princeton University


1d
comment On the existence of compactly supported functions whose its Fourier transform satisfies a given condition
In general, what you are asking about are functions in Gelfand-Shilov spaces. Perhaps there is something in the literature about these. I'd be extremely interested to know if it's true that if $\widehat{f} = O(e^{-k|\xi|^{\gamma}})$ for all $\gamma < 1$, then $\widehat{f}$ must be analytic on $\mathbb{R}$. But I don't know the answer.
1d
comment On the existence of compactly supported functions whose its Fourier transform satisfies a given condition
So if $\widehat{f}(\xi) = O(e^{-k|\xi|^{\gamma}})$ with $\gamma \geq 1$ and $k > 0$, then this same method works. But for $\gamma < 1$ this says nothing.
1d
comment On the existence of compactly supported functions whose its Fourier transform satisfies a given condition
The Paley-Wiener theorem shows that if $\widehat{f}(\xi) = O(e^{-k|\xi|})$ for some positive $k$, then $f$ extends to a holomorphic function in a horizontal strip containing $\mathbb{R}$, and so vanishes on an open set if and only if $f$ is uniformly zero.
1d
reviewed Reject suggested edit on An easy proof that S(n) does not embed into A(n+1)?
2d
reviewed Approve suggested edit on Intuition behind $\zeta(2) = \frac{\pi^2}{6}$
Oct
21
comment A good book on adeles and ideles
Goldfeld and Hundley, "Automorphic Representations and $L$-Functions for the General Linear Group" introduces the adeles (just over $\mathbb{Q}$, unfortunately) in some detail in the first chapter.
Oct
21
reviewed Approve suggested edit on Lemma on Polish Spaces
Oct
21
reviewed Approve suggested edit on When is fiber dimension upper semi-continuous?
Oct
20
reviewed Edit suggested edit on Lower bound of first moment of $L$-function on $\mathrm{GL}(3)$
Oct
20
revised Lower bound of first moment of $L$-function on $\mathrm{GL}(3)$
LaTeX the title and notation
Oct
18
reviewed Approve suggested edit on Is there any relationship between the Euler class and the Vandermonde determinant?
Oct
16
awarded  Suffrage
Oct
16
revised Is the Cassels-Tate pairing defined for elliptic curves over function fields?
edited title
Oct
16
reviewed Approve suggested edit on Lovasz theta function and independence number of product of simple odd-cycles
Oct
15
comment what would be the consequences on the distribution of primes of $\Lambda=\infty$?
Either spelling is acceptable. See here: english.stackexchange.com/questions/3824/…
Oct
15
reviewed Approve suggested edit on A simple proof that parallelizable oriented closed manifolds are oriented boundaries?
Oct
14
awarded  Curious
Oct
13
asked Weyl law for Maass forms with nontrivial character
Sep
29
reviewed Reject suggested edit on nontrivial theorems with trivial proofs
Sep
25
awarded  Excavator