The Poisson transform on a compact real analytic Riemannian manifold

被引：4

作者：

Stenzel, Matthew B. ^{[1
]}

机构：

[1] Ohio State Univ, Newark, OH 43055 USA

来源：

MONATSHEFTE FUR MATHEMATIK | 2015年 / 178卷 / 02期

关键词：

Poisson transform; Segal-Bargmann transform; Restriction principle; SEGAL-BARGMANN TRANSFORM; MONGE-AMPERE EQUATION; HEAT KERNEL TRANSFORM; SYMMETRIC-SPACES; NONCOMPACT TYPE; GRAUERT TUBES; COMPLEX TYPE; LIE-GROUPS; POLYNOMIALS;

D O I：

10.1007/s00605-015-0798-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the transform mapping an function f on a compact, real analytic Riemannian manifold X to the analytic continuation of to the interior of a Grauert tube tube about X. We show that after precomposing with an elliptic pseudodifferential operator this becomes a unitary map from onto the holomorphic functions on . If a compact Lie group of isometries acts transitively on X then the inverse of this unitarized map can be constructed by the restrict ion principle.

引用

页码：299 / 309

页数：11

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