The Poisson transform on a compact real analytic Riemannian manifold

被引:0
|
作者
Matthew B. Stenzel
机构
[1] The Ohio State University at Newark,
来源
Monatshefte für Mathematik | 2015年 / 178卷
关键词
Poisson transform; Segal–Bargmann transform; Restriction principle; 46F12; 35J05; 43A85;
D O I
暂无
中图分类号
学科分类号
摘要
We study the transform mapping an L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{2}$$\end{document} function f on a compact, real analytic Riemannian manifold X to the analytic continuation of exp(-tΔ)f\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\exp (-t \sqrt{\Delta })f$$\end{document} to the interior of a Grauert tube tube Mt\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_{t}$$\end{document} about X. We show that after precomposing with an elliptic pseudodifferential operator this becomes a unitary map from L2(X)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{2}(X)$$\end{document} onto the holomorphic L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{2}$$\end{document} functions on Mt\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_{t}$$\end{document}. 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
收藏
页码:299 / 309
页数:10
相关论文
共 50 条