Positive Definite Kernels on the Complex Hilbert Sphere.
Positive Q-matrices of graphs
The Q-matrix of a connected graph = (V,E) is , where ∂(x,y) is the graph distance. Let q() be the range of q ∈ (-1,1) for which the Q-matrix is strictly positive. We obtain a sufficient condition for the equality q(̃) = q() where ̃ is an extension of a finite graph by joining a square. Some concrete examples are discussed.
Positive-definite kernels, length functions on groups and a noncommutative von Neumann inequality
Property (T) and groups
We show that each group in a class of finitely generated groups introduced in [2] and [3] has Kazhdan’s property (T), and calculate the exact Kazhdan constant of with respect to its natural set of generators. These are the first infinite groups shown to have property (T) without making essential use of the theory of representations of linear groups, and the first infinite groups with property (T) for which the exact Kazhdan constant has been calculated. These groups therefore provide answers...
Property T for discrete groups in terms of their regular representation.
Property (T) for ... Factors and unitary representations of Kazhdan groups.
Propriétés des applications quadratiques d'un espace de Hilbert dans un espace vectoriel. Applications à la théorie spectrale des opérateurs normaux et à l'image numérique d'un opérateur
Pull-back properties of moment functions and a generalization of Bochner-Weil' s theorem.
Quotient groups of non-nuclear spaces for which the Bochner theorem fails completely
It is proved that every real metrizable locally convex space which is not nuclear contains a closed additive subgroup K such that the quotient group G = (span K)/K admits a non-trivial continuous positive definite function, but no non-trivial continuous character. Consequently, G cannot satisfy any form of the Bochner theorem.
Quotients de fonctions définies-négatives et synthèse spectrale
On considère l’espace où et sont deux fonctions définies-négatives, réelles et continues sur . On étudie la possibilité d’approcher, au sens de la norme de , tout élément de par des combinaisons linéaires d’éléments de qui sont transformés de Fourier de mesures positives de support inclus dans le spectre de . Des méthodes de théorie du potentiel permettent de donner une réponse positive (sous certaines hypothèses additionnelles). On obtient ainsi des généralisations, au cas de ,...
Relative Kazhdan property
Remarks on Characters of Discrete Nilpotent Groups.
Representations and Positive Definite Functions on Hypergroups
Some relationships between representations of a hypergroup X, its algebras, and positive definite functions on X are studied. Also, various types of convergence of positive definite functions on X are discussed.
Representations of involutive semigroups.
Resonance classes of measures.
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...