Eigenfunctions of the Laplace–Beltrami Operator on Harmonic NA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$NA$$\end{document} Groups

被引：0
作者：
Ewa Damek
Pratyoosh Kumar
机构：
[1] Wrocław University,Institute of Mathematics
[2] Indian Institute of Technology,Department of Mathematics
[3] Guwahati,undefined
来源：
The Journal of Geometric Analysis | 2016年 / 26卷 / 3期
关键词：
Eigenfunctions; Poisson transform; Harmonic ; group; Primary 43A85; Secondary 22E25;
D O I：
10.1007/s12220-015-9613-7
中图分类号：
学科分类号：
摘要：
We characterize some Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p$$\end{document}-type eigenfunctions of the Laplace–Beltrami operator on harmonic NA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$NA$$\end{document} groups corresponding to the eigenvalue (ρ2-β2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\rho ^2-\beta ^2)$$\end{document} for all β>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta >0$$\end{document}.
引用
收藏
页码：1913 / 1924
页数：11
相关论文
共 35 条
[1]  
Anker J-P(1996)Spherical analysis on harmonic Ann. Sc. Norm. Super. Pisa Cl. Sci. 23 643-679
[2]  
Damek E(1997) groups Bull. Aust. Math. Soc. 55 405-424
[3]  
Yacoub C(1991)The Helgason Fourier transform on a class of nonsymmetric harmonic spaces Adv. Math. 87 1-41
[4]  
Astengo F(1985)H-type groups and Iwasawa decompositions Trans. Am. Math. Soc. 290 375-384
[5]  
Camporesi R(1987)Harmonic functions on semidirect extensions of type Coll. Math. 53 255-268
[6]  
Di Blasio B(1987) nilpotent groups Coll. Math. 53 239-247
[7]  
Cowling MG(1992)Geometry of a semi-direct extension of a Heisenberg type nilpotent group Bull. Am. Math. Soc. (N.S.) 27 139-142
[8]  
Dooley AH(1963)A Poisson kernel on Heisenberg type nilpotent group Ann. Math. 77 335-386
[9]  
Korányi A(1972)A class of nonsymmetric harmonic Riemannian spaces Hiroshima Math. J. 2 535-545
[10]  
Ricci F(1970)A Poisson formula for semi-simple groups Adv. Math. 5 1-154
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