Ryszard Szwarc

An analytic family of uniformly bounded representations of free groups

Harmonic analysis on a free group F has attracted considerable attention in the last ten years or so. There seem to be two reason for that: one is the discovery of deep analogy of certain aspects of harmonic analysis on a free group and harmonic analysis on SL(2,R), cf. e.g. fundamental works of P. Cartier [4], A. Figa-Talamanca and M. A. Picardello [8], the other being the interest in the C∗-algebra generated by the regular representation of F , cf. A. Connes [5], J. Cuntz [6], U. Haagerup [10], M. Pimsner and D. Voiculescu [14].

On Axiomatization of Inconsistency Indicators for Pairwise Comparisons

This study examines the notion of inconsistency in pairwise comparisons for providing an axiomatization for it. It also proposes two inconsistency indicators for pairwise comparisons. The primary motivation for the inconsistency reduction is expressed by a computer industry concept “garbage in, garbage out”. The quality of the output depends on the quality of the input.

Orthogonal polynomials and a discrete boundary value problem II

Let

Connection coefficients of orthogonal polynomials

\{ {P_n } \}_{n = 0}^\infty

SCHUR MULTIPLIERS AND SPHERICAL FUNCTIONS ON HOMOGENEOUS TREES

be a system of polynomials orthogonal with respect to a measure

Linearization and connection coefficients of orthogonal polynomials

\mu

Groups Acting on Trees and Approximation Properties of the Fourier Algebra

on the real line. Then

Positivity of Turán Determinants for Orthogonal Polynomials

P_n

Convolution structures associated with orthogonal polynomials

satisfy the three-term recurrence formula

On the order of indeterminate moment problems

xP_n = \gamma _n P_{n + 1} + \beta _n P_n + \alpha _n P_{n - 1}