Second degree polynomials and the fundamental theorems of harmonic analysis.
Semi-groupes de moments.
Semi-groupes de moments sur un convexe compact de R...
Semigroups of measures in non-commutative analysis.
Semiperfect countable C-separative C-finite semigroups.
Semiperfect semigroups are abelian involution semigroups on which every positive semidefinite function admits a disintegration as an integral of hermitian multiplicative functions. Famous early instances are the group on integers (Herglotz Theorem) and the semigroup of nonnegative integers (Hamburger's Theorem). In the present paper, semiperfect semigroups are characterized within a certain class of semigroups. The paper ends with a necessary condition for the semiperfectness of a finitely generated...
Separation by characters or positive definite functions.
Stieltjes perfect semigroups are perfect
An abelian -semigroup is perfect (resp. Stieltjes perfect) if every positive definite (resp. completely so) function on admits a unique disintegration as an integral of hermitian multiplicative functions (resp. nonnegative such). We prove that every Stieltjes perfect semigroup is perfect. The converse has been known for semigroups with neutral element, but is here shown to be not true in general. We prove that an abelian -semigroup is perfect if for each there exist and such that ...
Strict positive definiteness on spheres via disk polynomials.
Structure of Blaschke cocycles
Sur l'espace de Banach engendré par les coefficients d'une représentation unitaire