The partial Legendre transformation for plurisubharmonic functions
The partial Legendre transformation for plurisubharmonic functions
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DOI：
10.1007/bf01403083
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发表时间：
1978-06
影响因子：
3.1
通讯作者：
C. Kiselman
中科院分区：
文献类型：
--
作者：
C. Kiselman
凸集的线性图像是凸的，但尽管凸性和伪凸性之间存在深远的类比，但相应的结果在复数域中并不成立：C a 中的伪凸集在 C 2 中的投影可能不是伪凸的。本文的目的是展示一类允许伪凸的伪凸集 投影并研究相关的函数变换，即部分勒让德变换。我们希望这种变换可以用于研究多次谐波函数的局部行为。
A linear image of a convex set is convex, but in spite of the farreaching analogy between convexity and pseudoconvexity the corresponding result is not true in the complex domain: the projection in C 2 of a pseudoconvex set in C a may fail to be pseudoconvex.The purpose of the present paper is to exhibit a class of pseudoconvex sets which admit pseudoconvex projections and to study an associated functional transformation, the partial Legendre transformation. We hope that this transformation can be used to study eg the local behavior of plurisubharmonic functions.