All Questions
Tagged with estimation-theory fa.functional-analysis
4 questions with no upvoted or accepted answers
3
votes
0
answers
113
views
Image restoration quality general lower bounds
A typical image restoration model posits that, starting from a true image $f = f(x,y)$, we observe
$$
\tilde f = f \star h + n
$$
where $\star$ is convolution, $h$ is the point spread function (caused,...
2
votes
0
answers
122
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Comparing the truncated $\ell^{1}$-norm of polynomial coefficients with the supremum norm on the unit disc
Let $p=a_{0}+a_{1}z+\ldots+a_{n}z^{n}$ be a polynomial. Consider the following truncated $\ell^{1}$-seminorm of the coefficients of $p$:
$$\|p\|_{\ell^{1},\text{trun.}}:=\sum_{k=1}^{n}|a_{k}|=\|p-a_{0}...
2
votes
0
answers
225
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Sobolev (Triebel-Lizorkin) norm estimate for $F \circ u - F \circ v$
Let $F \in C^1(\mathbb R^d;\mathbb R)$ be such that $F(0) = 0$ and
$$|F'(\tau v + (1 - \tau)w)| \leq \mu(\tau)(G(v) + G(w))$$
for some $\mu \in L^1([0,1])$ and some non-negative $G \in C^0(\mathbb R^d;...
0
votes
0
answers
21
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Estimatives for elliptic systems involving the laplacian
Considering the problem
\begin{equation}
\left\{
\begin{array}[c]{11}
\Delta(\Delta \chi -\chi) = 0 & \text{in } \Omega, \\
\Delta \chi -\chi = h_2 - h_1, & \text{on } \partial\Omega \\
\end{...