bio | website | math.ucla.edu/~mlewko |
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location | ||
age | ||
visits | member for | 5 years |
seen | 16 mins ago | |
stats | profile views | 3,842 |
Oct 18 |
awarded | Yearling |
Oct 13 |
answered | $L^2$ boundedness of the Hilbert transform via Cotlar-Stein Lemma |
Jul 6 |
answered | Proof of the Friedlanderâ€“Iwaniec theorem |
Jul 2 |
awarded | Curious |
May 5 |
comment |
Distribution of $a^2+\alpha b^2$
This isn't an answer, but there is a theorem of Atkin which is in a similar spirit: These exists a sequence of integers such that the n-th term is $n^2 + O(log(n))$ and whose sumset has positive density in the integers. ams.org/mathscinet-getitem?mr=202687 |
Apr 29 |
answered | A question on Cramer's theorem |
Apr 9 |
comment |
Fourier series of functions on compact groups
@Anton, If you interpret the question like that it isn't very interesting. There are certainly $L^2$ functions on the circle without absolutely convergent Fourier series. You could alternately ask for unconditional pointwise convergence (that is a.e. pointwise convergence for every ordering) but this is false for every complete infinite orthonormal system (such as Fourier series on the cirlce, again). |
Apr 9 |
comment |
Fourier series of functions on compact groups
How are you ordering the summation? Note that one must specify an ordering before it makes sense to talk about pointwise convergence. |
Apr 3 |
awarded | Nice Answer |
Feb 20 |
comment |
Objections to and arguments for the simplicity of all Riemann zeros
Micah, can you give a reference for this? Is the same known for $\psi$? |
Feb 20 |
awarded | Nice Answer |
Feb 19 |
answered | Carleson-Hunt inequality: changing order of summation |
Feb 18 |
revised |
Finite field Szemeredi-Trotter theorem with unequal number of points and lines
added 651 characters in body |
Feb 18 |
answered | Finite field Szemeredi-Trotter theorem with unequal number of points and lines |
Feb 14 |
revised |
Result of Beurling concerning absolute convergence of Fourier series of |f|
added 21 characters in body |
Feb 14 |
answered | Result of Beurling concerning absolute convergence of Fourier series of |f| |
Feb 10 |
answered | When is the bound in Riesz-Thorin Interpolation Theorem attained? |
Feb 10 |
awarded | Fanatic |
Jan 30 |
answered | Number of Totally Isotropic Subspaces |
Jan 15 |
comment |
Carleson's Theorem on Manifolds
Note that the answer will depend on how you order the eigenfunctions. Ordering by eigenvalue is perhaps the most natural choice. In the case of the the $2$-d torus this gives spherical summation for $2$ dimensional Fourier series. Determining if pointwise convergence holds in this setting is a longstanding open problem. |