强渐近$\ell_p$空间与极小性

渐近\ell_^ 1巴拿赫空间的例子

Examples of asymptotically \ell_^1 Banach spaces

给出了渐近$\ell_{1}$巴拿赫空间的两个例子。第一个是$X_{u}$，它有一个无条件基，并且是任意可变形的。第二个是$X$，它不包含任何无条件的基本序列。两者都是Tsirelson类型的空间。因此，我们回答了高尔斯提出的一个问题。

渐近$\ell_1$空间中$\ell_1$的邻近性和偏差

Proximity to $\ell_1$ and Distortion in Asymptotic $\ell_1$ Spaces

对于具有基$(x_i)$的渐近$\ell_1$空间$X$，为$α<ω_1$定义了某些渐近$\ell_1$常数，$δ_α(X)$。$δ_α(X)$度量$(x_i)$的所有规范化块基$(y_i)_{i=1}^k$之间的等价性，这些块基相对于$(x_i)$是$S_α$ -容许的（$S_α$是集合的$α^{th}$类），并且是$\ell_1^k$的单位向量基。这导致了$X$的δ谱的概念，$Δ(X)$，它反映了$δ_α(X)$的稳定极限的行为。这些常数下的所有重整$X$的类似物也被定义和研究。我们调查$Δ(X)$在一般情况下和有界失真的空间。我们还证明了几个结果扭曲经典Tsirelson的空间$T$及其亲属。

The complete separation of the two finer asymptotic $\ell_{p}$ structures for $1\le p<\infty$

For $1\le p <\infty$, we present a reflexive Banach space $\mathfrak{X}^{(p)}_{\text{awi}}$, with an unconditional basis, that admits $\ell_p$ as a unique asymptotic model and does not contain any Asymptotic $\ell_p$ subspaces. D. Freeman, E. Odell, B. Sari and B. Zheng have shown that whenever a Banach space not containing $\ell_1$, in particular a reflexive Banach space, admits $c_0$ as a unique asymptotic model then it is Asymptotic $c_0$. These results provide a complete answer to a problem posed by L. Halbeisen and E. Odell and also complete a line of inquiry of the relation between speci…

渐近$\ell_p$空间上不是单位重数紧扰动的算子

Operators on Asymptotic $\ell_p$ Spaces which are not Compact Perturbations of a Multiple of the Identity

本文给出了渐近$\ell_p$（对于$1 < p < \infty$）巴拿赫空间上的充分条件，该条件保证了空间中存在一个不是恒等式的倍数的紧扰动的算子.这些条件意味着在G. Androulakis和作者和我。Deliyanni和A. Manoussakis此外，我们证明了在这些相同的条件下，空间$X$，$\ell_\infty$同构嵌入到空间的有界线性算子$X$。

Positive Liouville theorem and asymptotic behaviour for $(p,A)$-Laplacian type elliptic equations with Fuchsian potentials in Morrey space

We study Liouville-type theorems and the asymptotic behaviour of positive solutions near an isolated singular point $ζ\in\partialΩ\cup\{\infty\}$ of the quasilinear elliptic equations $$-\text{div}(|\nabla u|_A^{p-2}A\nabla u)+V|u|^{p-2}u =0\quad\text{in } Ω\setminus\{ζ\},$$ where $Ω$ is a domain in $\mathbb{R}^d$ ($d\geq 2$), and $A=(a_{ij})\in L_{\rm loc}^{\infty}(Ω;\mathbb{R}^{d\times d})$ is a symmetric and locally uniformly positive definite matrix. The potential $V$ lies in a certain local Morrey space (depending on $p$) and has a Fuchsian-type isolated singularity at $ζ$.

$\ell_1$范数支持向量机的非渐近性分析

Non-asymptotic Analysis of $\ell_1$-norm Support Vector Machines

带$\ell_1$惩罚的支持向量机（Support Vector Machines，SVM）在生物信息学和信号处理等领域成为分析具有稀疏约束的高维分类问题的标准工具。虽然支持向量机已被深入研究的文献中，本文有我们所知的第一个非渐近结果的性能$\ell_1$ -支持向量机在识别稀疏分类器。我们表明，$d$维$s$稀疏分类向量可以（以高概率）很好地近似只有$O(s\log(d))$高斯试验。证明中使用的方法包括测度集中和Banach空间中的概率。