Uniformly Amenable Discrete Groups.
Remark on Herz-Schur Multipliers on Free Groups.
Uniformly bounded representations of free groups.
Some aspects of harmonic analysis on free groups
Sets of uniqueness on noncommutative locally compact groups. II
Completely positive maps on Coxeter groups and the ultracontractivity of the q-Ornstein-Uhlenbeck semigroup
Positive-definite kernels, length functions on groups and a noncommutative von Neumann inequality
A new group algebra and lacunary sets in discrete noncommutative groups
Littlewood functions, Hankel multipliers and power bounded operators on a Hilbert space
Remarks on q-CCR relations for |q| > 1
In this paper we give a construction of operators satisfying q-CCR relations for q > 1: and also q-CAR relations for q < -1: , where N is the number operator on a suitable Fock space acting as Nx₁ ⊗ ⋯ ⊗ xₙ = nx₁ ⊗ ⋯ ⊗xₙ. Some applications to combinatorial problems are also given.
Completely positive maps on Coxeter groups, deformed commutation relations, and operator spaces.
Interpolations between bosonic and fermionic relations given by generalized Brownian motions.
New Examples of Convolutions and Non-Commutative Central Limit Theorems
A family of transformations on the set of all probability measures on the real line is introduced, which makes it possible to define new examples of convolutions. The associated central limit theorems are studied, and examples of the limit measures, related to the classical, free and boolean convolutions, are shown.
Remarks on t-transformations of measures and convolutions
A note on certain partial sum operators
We show that for the t-deformed semicircle measure, where 1/2 < t ≤ 1, the expansions of functions with respect to the associated orthonormal polynomials converge in norm when 3/2 < p < 3 and do not converge when 1 ≤ p < 3/2 or 3 < p. From this we conclude that natural expansions in the non-commutative spaces of free group factors and of free commutation relations do not converge for 1 ≤ p < 3/2 or 3 < p.
Generalized q-deformed Gaussian random variables
We produce generalized q-Gaussian random variables which have two parameters of deformation. One of them is, of course, q as for the usual q-deformation. We also investigate the corresponding Wick formulas, which will be described by some joint statistics on pair partitions.
Topics on Meixner families
We shed some light on the inter-connections between different characterizations leading to the classical Meixner family. This allows us to give free analogs of both Sheffer's and Al-Salam and Chihara's characterizations in the classical case by the use of the free derivative operator. The paper closes with a discussion of the q-deformed case, |q| < 1.
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