The Pontryagin dual of the multiplicative group of positive rational numbers

Chaochao Sun; Yuanbo Liu; Chaochao Sun; Yuanbo Liu

doi:10.3934/math.20231037

AIMS Mathematics

2023, Volume 8, Issue 9: 20351-20360. doi: 10.3934/math.20231037

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The Pontryagin dual of the multiplicative group of positive rational numbers

Chaochao Sun ^{1
,
,},
Yuanbo Liu ²

1.
School of Mathematics and Statistics, Linyi University, Linyi 276005, China
2.
School of Mathematics and Information, China West Normal University, Nanchong 637009, China

Received: 09 January 2023 Revised: 06 June 2023 Accepted: 07 June 2023 Published: 21 June 2023
MSC : 11M06, 11R42

The Pontryagin dual of the multiplicative group of positive rational numbers is constructed. Then we study its topological generators and representations.
- Pontryagin dual,
- topological generator,
- Hilbert space,
- representation
Citation: Chaochao Sun, Yuanbo Liu. The Pontryagin dual of the multiplicative group of positive rational numbers[J]. AIMS Mathematics, 2023, 8(9): 20351-20360. doi: 10.3934/math.20231037

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Abstract

The Pontryagin dual of the multiplicative group of positive rational numbers is constructed. Then we study its topological generators and representations.

References

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