2
votes
2answers
143 views

Non-global oscillation of banded Fourier transform

Can we say something like monotonicity, growth rate and oscillation of the Fourier transform of a banded function $f$ with support $[0, N]$ $$\mathcal{F}f(\xi) = \int_{0}^N f(x)e^{-ix\xi}dx.$$ Of ...
2
votes
1answer
314 views

A question about the Beurling-Selberg majorant

Beurling's majorant is defined as the unique entire function $B(z)$ such that the Fourier transform of $B(x)$ is compactly supported in the interval $[-1;1]$, $B(x) \geq \text{sgn}(x)$ and $B(x)$ ...
5
votes
2answers
891 views

L1 distance from a trigonometric susbspace

How to check, whether the $L^{1}$ distance between a finite exponential sum $S_{F}(x)=\sum\limits_{n\in F} \exp(inx)$ and the $L^{1}$-closure of subspace $\mathrm{span}\left(\exp(inx): n\in ...