Surjectivity of mean value operators on noncompact symmetric spaces

被引：4

作者：

Christensen, Jens ^{[1
]}

Gonzalez, Fulton ^{[2
]}

Kakehi, Tomoyuki ^{[3
]}

机构：

[1] Colgate Univ, Dept Math, Hamilton, NY 13346 USA

[2] Tufts Univ, Dept Math, Medford, MA 02155 USA

[3] Univ Tsukuba, Div Math, Tsukuba, Ibaraki 3058571, Japan

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2017年 / 272卷 / 09期

关键词：

Mean value operators; Noncompact symmetric spaces; TRANSFORM; DIVISION; THEOREM;

D O I：

10.1016/j.jfa.2016.12.022

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let X = G/K be a symmetric space of the noncompact type. We prove that the mean value operator over translated K-orbits of a fixed point is surjective on the space of smooth functions on X if X is either complex or of rank one. For higher rank spaces it is shown that the same statement is true for points in an appropriate Weyl subchamber. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：3610 / 3646

页数：37

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