| File | |
| Title |
一般線形GL(k;R)の表現と球関数
|
| Title |
On a Representation of The Group GL (k;R) and Its Spherical Functions
|
| Title Transcription |
イッパン センケイ GL K R ノ ヒョウゲン ト キュウカンスウ
|
| Creator |
Asoo Yasuhiro
|
| Source Title |
島根大学文理学部紀要. 理学科編
Memoirs of the Faculty of Literature and Science, Shimane University. Natural sciences
|
| Volume | 4 |
| Start Page | 10 |
| End Page | 26 |
| Journal Identifire |
ISSN 03709434
|
| Descriptions |
Abstract
In 1961, A. T. James [1] introduced the zonal polynomial of real positive definite matrix and he described some properties and a method of calculation of it. Lately, he [2] also showed that it is an eigenfunction of the Laplace-Beltrami operator. The zonal polynomial plays significant roles in distribution problems of eigenvalues related to the normal multivariate distribution [3]. In the present paper, we will describe a representation of the group GL (k ; R) and its spherical functions guided by N. J. Vilenkin [4]. Our assumptions 1 and 2 in the following may be satisfied with zonal polynomials. We also give a definition of (zonal) spherical function of the group GL (k ; R) guided by K. Maurin [5] and we show that our zonal spherical function is in agreement with the latter definition.
|
| Language |
eng
|
| Resource Type | departmental bulletin paper |
| Publisher |
島根大学文理学部
The Faculty of Literature and Science, Shimane University
|
| Date of Issued | 1971-03-15 |
| Access Rights | open access |
| Relation |
[NCID]
AN0010806X
|
