功能Donoho-Stark-Elad-Bruckstein-Ricaud-Torrésani不确定性原理
Functional Donoho-Stark-Elad-Bruckstein-Ricaud-Torrésani Uncertainty Principle
AI总结：
本文提出功能Donoho-Stark-Elad-Bruckstein-Ricaud-Torrésani不确定性原理，改进了Ricaud-Torrésani、Elad-Bruckstein和Donoho-Stark不确定性原理，通过p-Schauder框架的性质建立新的不等式。
摘要：
本文提出功能Donoho-Stark-Elad-Bruckstein-Ricaud-Torrésani不确定性原理，改进了Ricaud-Torrésani、Elad-Bruckstein和Donoho-Stark不确定性原理，通过p-Schauder框架的性质建立新的不等式。
英文摘要：
Let $(\{f_j\}_{j=1}^n, \{τ_j\}_{j=1}^n)$ and $(\{g_k\}_{k=1}^m, \{ω_k\}_{k=1}^m)$ be p-Schauder frames for a finite dimensional Banach space $\mathcal{X}$. Then for every $x \in \mathcal{X}\setminus\{0\}$, we show that \begin{align} (1) \quad \|θ_f x\|_0^\frac{1}{p}\|θ_g x\|_0^\frac{1}{q} \geq \frac{1}{\displaystyle\max_{1\leq j\leq n, 1\leq k\leq m}|f_j(ω_k)|}\quad \text{and} \quad \|θ_g x\|_0^\frac{1}{p}\|θ_f x\|_0^\frac{1}{q}\geq \frac{1}{\displaystyle\max_{1\leq j\leq n, 1\leq k\leq m}|g_k(τ_j)|}. \end{align} where \begin{align*} θ_f: \mathcal{X} \ni x \mapsto (f_j(x) )_{j=1}^n \in \ell^p([n]); \quad θ_g: \mathcal{X} \ni x \mapsto (g_k(x) )_{k=1}^m \in \ell^p([m]) \end{align*} and $q$ is the conjugate index of $p$. We call Inequality (1) as \textbf{Functional Donoho-Stark-Elad-Bruckstein-Ricaud-Torrésani Uncertainty Principle}. Inequality (1) improves Ricaud-Torrésani uncertainty principle \textit{[IEEE Trans. Inform. Theory, 2013]}. In particular, it improves Elad-Bruckstein uncertainty principle \textit{[IEEE Trans. Inform. Theory, 2002]} and Donoho-Stark uncertainty principle \textit{[SIAM J. Appl. Math., 1989]}.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
