bio | website | math.ucla.edu/~mlewko |
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visits | member for | 4 years, 6 months |
seen | 4 hours ago | |
stats | profile views | 3,674 |
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
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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|
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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. |
Jan 6 |
answered | Higher dimensional generalization of the Hardy-Littlewood conjecture? |
Jan 6 |
revised |
Strong decomposition tools from Harmonic Analysis in other fields
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Jan 6 |
answered | Strong decomposition tools from Harmonic Analysis in other fields |
Jan 6 |
revised |
Reference and best bounds of $\sum_{n\leq x}\frac{\mu(n)}{n}$
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Jan 6 |
answered | Reference and best bounds of $\sum_{n\leq x}\frac{\mu(n)}{n}$ |
Jan 4 |
comment |
The example of mechanical system that has a Mobius strip as their configuration space
There are also applications of Mobius strips to electrical systems, see the Mobius resistor: en.wikipedia.org/wiki/M%C3%B6bius_resistor |