| 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
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| Title Alternative (English) | On a Representation of The Group GL (k;R) and Its Spherical Functions
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| File | |
| language |
eng
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| Author |
Asoo, Yasuhiro
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| Description | 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.
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| Journal Title |
Memoirs of the Faculty of Literature and Science, Shimane University. Natural sciences
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| Volume | 4
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| Start Page | 10
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| End Page | 26
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| ISSN | 03709434
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| Published Date | 1971-03-15
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| NCID | AN0010806X
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| Publisher | 島根大学文理学部
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| Publisher Aalternative | The Faculty of Literature and Science, Shimane University
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| NII Type |
Departmental Bulletin Paper
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| OAI-PMH Set |
Faculty of Science and Engineering
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| 他の一覧 |
