THE LAPLACIAN AND THE HEAT KERNEL ACTING ON DIFFERENTIAL FORMS ON SPHERES

被引：0

作者：

Nagase, Masayoshi ^{[1
]}

机构：

[1] Saitama Univ, Grad Sch Sci & Engn, Dept Math, Saitama 3388570, Japan

来源：

TOHOKU MATHEMATICAL JOURNAL | 2009年 / 61卷 / 04期

基金：

日本学术振兴会;

关键词：

Sphere; Laplacian; heat kernel; RIEMANNIAN SYMMETRIC-SPACES; COMPACT; 1-FORMS; SPECTRA;

D O I：

10.2748/tmj/1264084500

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the Laplacian acting on differential forms on a sphere can be lifted to an operator on its rotation group which is intrinsically equivalent to the Laplacian acting on functions on the Lie group. Further, using the result and the Urakawa summation formula for the heat kernel of the latter Laplacian and the Weyl integration formula, we get a summation formula for the kernel of the former.

引用

页码：571 / 588

页数：18

共 16 条

[1] ABE K, 1997, TOKYO J MATH, V20, P87
[2] [Anonymous], PURE APPL MATH
[3] [Anonymous], 1983, SEMIRIEMANNIAN GEOME
[4] [Anonymous], PURE APPL MATH
[5] [Anonymous], 1941, Progress in Mathematics
[6] BENABDALLAH AI, 1973, B SOC MATH FR, V101, P265
[7] Chavel Isaac, 1984, EIGENVALUES RIEMANNI
[8] Eskin L.D., 1964, Memoriam, P113
[9] IKEDA A, 1978, OSAKA J MATH, V15, P515
[10] THE SPECTRA OF 1-FORMS ON SIMPLY CONNECTED COMPACT IRREDUCIBLE RIEMANNIAN SYMMETRIC-SPACES .2.
KANEDA, E
[J]. JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 1984, 24 (01): : 141 - 162

← 1 2 →