### 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 language | English |
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Pages (from-to) | 415-422 |

Number of pages | 8 |

Journal | Journal of the Australian Mathematical Society |

Volume | 46 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1989 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

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

Research output: Contribution to journal › Article

*Journal of the Australian Mathematical Society*, vol. 46, no. 3, pp. 415-422. https://doi.org/10.1017/S1446788700030901

}

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 -