STRONG CONVEXITY FOR HARMONIC FUNCTIONS ON COMPACT SYMMETRIC SPACES

被引：0

作者：

Lippner, Gabor ^{[1
]}

Mangoubi, Dan ^{[2
]}

Mcguirk, Zachary ^{[2
]}

Yovel, Rachel ^{[2
]}

机构：

[1] Northeastern Univ, Dept Math, 360 Huntington Ave, Boston, MA 02115 USA

[2] Hebrew Univ Jerusalem, Einstein Inst Math, Edmond J Safra Campus, IL-91904 Jerusalem, Israel

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2022年 / 150卷 / 04期

关键词：

Symmetric spaces; harmonic functions; Laplace powers; frequency; function; absolute monotonicity; convexity;

D O I：

10.1090/proc/15735

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let h be a harmonic function defined on a spherical disk. It is shown that Delta k|h|2 is nonnegative for all k is an element of N where Delta is the Laplace-Beltrami operator. This fact is generalized to harmonic functions defined on a disk in a normal homogeneous compact Riemannian manifold, and in particular in a symmetric space of the compact type. This complements a similar property for harmonic functions on Rn discovered by the first two authors and is related to strong convexity of the L2-growth function of harmonic functions.

引用

页码：1613 / 1622

页数：10

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