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On the Haagerup inequality and groups acting on A ˜ n -buildings

Alain Valette (1997)

Annales de l'institut Fourier

Let Γ be a group endowed with a length function L , and let E be a linear subspace of C Γ . We say that E satisfies the Haagerup inequality if there exists constants C , s > 0 such that, for any f E , the convolutor norm of f on 2 ( Γ ) is dominated by C times the 2 norm of f ( 1 + L ) s . We show that, for E = C Γ , the Haagerup inequality can be expressed in terms of decay of random walks associated with finitely supported symmetric probability measures on Γ . If L is a word length function on a finitely generated group Γ , we show that,...

On the Stieltjes moment problem on semigroups

Torben Maack Bisgaard (2002)

Czechoslovak Mathematical Journal

We characterize finitely generated abelian semigroups such that every completely positive definite function (a function all of whose shifts are positive definite) is an integral of nonnegative miltiplicative real-valued functions (called nonnegative characters).

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