加权$θ$ -不完全多能理论

加权多项式与加权多势理论

Weighted polynomials and weighted pluripotential theory

本文研究了C^N中紧集E上的加权多势与C^（N+1）中相伴圈集Z上的多势理论之间的关系

复Kähler流形上的加权多位势理论

Weighted pluripotential theory on complex Kähler manifolds

我们介绍了一个加权版本的多能理论的复杂Kähler流形开发的Guedj和Zeriahi。给出了加权复格林函数的适当定义、基本性质，并讨论了它在全纯映射下的性质。我们还建立了Siciak的H-原理的推广。

Berman-Boucksom的加权多势理论结果

Weighted Pluripotential Theory Results of Berman-Boucksom

这些笔记的主要目标是在2008-2009年编写的，是对R。Berman和S. Boucksom在加权多能理论的背景下。我们包括一些背景结果的多能性理论和加权多能性理论，虽然许多项目没有证明（提供参考）。虽然有点过时，当然也不是没有错误，我们希望有人发现他们有帮助。

Pluripotential Theory and Convex Bodies

In their seminal paper, Berman and Boucksom exploited ideas from complex geometry to analyze asymptotics of spaces of holomorphic sections of tensor powers of certain line bundles $L$ over compact, complex manifolds as the power grows. This yielded results on weighted polynomial spaces in weighted pluripotential theory in $\Bbb{C}^d$. Here, motivated from Bayraktar's recent paper, we work in the setting of weighted pluripotential theory arising from polynomials associated to a convex body in $(\Bbb{R}^+)^d$. These classes of polynomials need not occur as sections of tensor powers of a line bun…

向量值函数与微分形式多项式插值的多势理论框架

A pluripotential theoretic framework for polynomial interpolation of vector-valued functions and differential forms

本文提出修正的加权多势理论框架，引入向量值权重，将标量值函数插值的渐近结果部分推广到有限维复内积空间中的向量值函数，并应用于微分形式的多项式系数插值。

Pluripotential Theory and Convex Bodies: Large Deviation Principle

We continue the study in a previous work in the setting of weighted pluripotential theory arising from polynomials associated to a convex body $P$ in $({\bf R}^+)^d$. Our goal is to establish a large deviation principle in this setting specifying the rate function in terms of $P-$pluripotential-theoretic notions. As an important preliminary step, we first give an existence proof for the solution of a Monge-Ampère equation in an appropriate finite energy class. This is achieved using a variational approach.