All Questions
5 questions
0
votes
0
answers
57
views
Double-periodic functions with (possible) poles
Consider the set of double-periodic function $f:\mathbb C/(\mathbb Z+i \mathbb Z) \setminus \{z_0\} \to \mathbb C$, where $z_0$ is a fixed point inside $\mathbb C/(\mathbb Z+i \mathbb Z),$ that have a ...
7
votes
1
answer
665
views
Dominated convergence to characteristic function
Let $\phi_m(x):=\chi_{[0,1]} * \chi_{[0,1]} *...* \chi_{[0,1]}$ be the m -times convolution (so $m+1$ characteristic functions are involved).
Then the Fourier transform of this function is given by
$...
13
votes
2
answers
862
views
Motivation for BMO
At the moment, I don't have access to the early 1960's paper of John and Nirenberg that (from what I understand) introduced the space BMO (bounded mean oscillation). Why were John and Nirenberg ...
3
votes
6
answers
1k
views
Reference for complex analysis jargon
I am not a (complex) analyst but it seems that some of the questions I am working on are related to the following concepts:
logarithmic capacity
transfinite diameter
Green's function of a compact ...
2
votes
1
answer
227
views
Interpolating delta like functions by trigonometric polynomials of bounded modulus and fast decay
Consider a grid of points $T=\{t_0,t_1,\ldots,t_m\}$ with $0\le t_i\le 1$. I would like to find a function $f(t):[0,1]\rightarrow \mathbb{C}$ of the form
\begin{equation*}
f(t)=\sum_{k=-n}^n c_k e^{2\...