Fourier inversion formula for discrete nilpotent groups

Research output: Contribution to journalArticle

Abstract

Let G be a countable torsion free finitely generated nilpotent group. Then the Fourier transform can be considered as a map from the space of bounded degree 1 random operators to the Fourier algebra A(G). In this paper, we recover the matrix elements of a positive random variable from the corresponding positive definite function in A(G) for such a group. 1980 Mathematics subject classification (Amer. Math. Soc.): 46 L 55.

Original languageEnglish
Pages (from-to)415-422
Number of pages8
JournalJournal of the Australian Mathematical Society
Volume46
Issue number3
DOIs
Publication statusPublished - 1989

Fingerprint

Fourier Algebra
Random Operators
Positive Definite Functions
Inversion Formula
Finitely Generated Group
Nilpotent Group
Discrete Group
Torsion-free
Countable
Fourier transform
Random variable

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Fourier inversion formula for discrete nilpotent groups. / Kajiwara, Tsuyoshi.

In: Journal of the Australian Mathematical Society, Vol. 46, No. 3, 1989, p. 415-422.

Research output: Contribution to journalArticle

@article{b61ddcc038124434b2f63e6769019843,
title = "Fourier inversion formula for discrete nilpotent groups",
abstract = "Let G be a countable torsion free finitely generated nilpotent group. Then the Fourier transform can be considered as a map from the space of bounded degree 1 random operators to the Fourier algebra A(G). In this paper, we recover the matrix elements of a positive random variable from the corresponding positive definite function in A(G) for such a group. 1980 Mathematics subject classification (Amer. Math. Soc.): 46 L 55.",
author = "Tsuyoshi Kajiwara",
year = "1989",
doi = "10.1017/S1446788700030901",
language = "English",
volume = "46",
pages = "415--422",
journal = "Journal of the Australian Mathematical Society",
issn = "1446-7887",
publisher = "Cambridge University Press",
number = "3",

}

TY - JOUR

T1 - Fourier inversion formula for discrete nilpotent groups

AU - Kajiwara, Tsuyoshi

PY - 1989

Y1 - 1989

N2 - Let G be a countable torsion free finitely generated nilpotent group. Then the Fourier transform can be considered as a map from the space of bounded degree 1 random operators to the Fourier algebra A(G). In this paper, we recover the matrix elements of a positive random variable from the corresponding positive definite function in A(G) for such a group. 1980 Mathematics subject classification (Amer. Math. Soc.): 46 L 55.

AB - Let G be a countable torsion free finitely generated nilpotent group. Then the Fourier transform can be considered as a map from the space of bounded degree 1 random operators to the Fourier algebra A(G). In this paper, we recover the matrix elements of a positive random variable from the corresponding positive definite function in A(G) for such a group. 1980 Mathematics subject classification (Amer. Math. Soc.): 46 L 55.

UR - http://www.scopus.com/inward/record.url?scp=84974401756&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84974401756&partnerID=8YFLogxK

U2 - 10.1017/S1446788700030901

DO - 10.1017/S1446788700030901

M3 - Article

AN - SCOPUS:84974401756

VL - 46

SP - 415

EP - 422

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

SN - 1446-7887

IS - 3

ER -