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This article is cited in 1 scientific paper (total in 1 paper)
Weight functions on groups and an amenability criterion for Beurling algebras
R. I. Grigorchuk Steklov Mathematical Institute, Russian Academy of Sciences
Abstract:
The paper is devoted to the study of weights on groups. A connection between weight functions and harmonic functions is established. A relationship between the weight theory on groups with the “Tychonoff property” and the theory of bounded cohomology is presented.
It is proved that the Beurling algebra $l^1(G,\omega)$ constructed for the weight $\omega$ is amenable if and only if the group $G$ is amenable and the weight $\omega$ is equivalent to a multiplicative character $\chi\colon G\to\mathbb R_+$.
DOI:
https://doi.org/10.4213/mzm1837
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English version:
Mathematical Notes, 1996, 60:3, 274–282
Bibliographic databases:
UDC:
512 Received: 27.12.1995
Citation:
R. I. Grigorchuk, “Weight functions on groups and an amenability criterion for Beurling algebras”, Mat. Zametki, 60:3 (1996), 370–382; Math. Notes, 60:3 (1996), 274–282
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/mz1837https://doi.org/10.4213/mzm1837 http://mi.mathnet.ru/eng/mz/v60/i3/p370
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Shtern, AI, “Triviality and continuity of pseudocharacters and pseudorepresentations”, Russian Journal of Mathematical Physics, 5:1 (1997), 135
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