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Results tagged with fourier-analysis
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user 90189
The representation of functions (or objects which are in some generalize the notion of function) as constant linear combinations of sines and cosines at integer multiples of a given frequency, as Fourier transforms or as Fourier integrals.
7
votes
Support of function and support of its Fourier transform
This is a delayed answer, but it seems good to clarify what the OP is asking. This kind of statements: "since $f$ is concentrated in such a ball then its Fourier transform is essentially concentrated …
- 408
1
vote
Accepted
On a paper by Adams and Frazier
I'm not quite confident about what I'll write, but I think that there is an issue here. I haven't read the paper, but I'd suggest the following amendment:
By Hölder, with exponents $q$ and $q'$, to b …
- 408
0
votes
Fourier support condition in the paper 'A study guide for the $l^2$ decoupling theorem'
For any function $f$, since $\hat{f}(x,y,z)=\int f(\xi_1,\xi_2,\xi_3)e(-\langle (x,y,z), \xi\rangle)\,d\xi$, for fixed $y$ we have that the function $(x,z)\mapsto \hat{f}(x,y,z)$ is the Fourier transf …
- 408
2
votes
Accepted
Idea behind Carleson's theorem modern proof "intitial reductions"
I have my own confusions here, but let me share my thoughts.
As you mention, there is a discretization here. If you want to decompose the operator $P_-$, you use the standard decomposition $\sum_k\ha …
- 408