scholarly journals Extending positive definite functions from subgroups of nilpotent locally compact groups

2017 ◽  
Vol 272 (2) ◽  
pp. 559-576
Author(s):  
Eberhard Kaniuth
Keyword(s):  
Positive Definite ◽  
Positive Definite Functions ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact

scholarly journals On Godement's characterisation of amenability

1998 ◽  
Vol 57 (1) ◽  
pp. 153-158 ◽  
Author(s):  
Alain Valette
Keyword(s):  
Positive Definite Function ◽  
Positive Definite ◽  
Locally Compact Groups ◽  
Definite Function ◽  
Compact Groups ◽  
Locally Compact ◽  
Unimodular Group ◽  
Compactly Supported ◽  
Assembly Map

Motivated by a question related to the construction of the Baum-Connes analytical assembly map for locally compact groups, we refine a criterion of Godement for amenability: for a unimodular group G, our criterion says that G is amenable if and only if every compactly supported, positive-definite function has non-negative integral over G.

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