Based on the theory of spherical harmonics for measures invariant under a finite reflection group developed by Dunkl recently, we study orthogonal polynomials with respect to the weight functions jx1jã1 Ð Ð Ð jxdjãd on the unit sphere Sd 1 in Rd. The results include explicit formulae for orthonormal polynomials, reproducing and Poisson kernel, as well as intertwining operator.

Purpose Paley's and Hardy's inequality are proved on a Hardy-type space for the Fourier–Dunkl expansions based complete orthonormal system of Dunkl kernels generalizing classical exponential defining Fourier series. Design/methodology/approach Although difficulties related to settings, techniques used by K. Sato were still efficient in this case establish inequalities which have expected simila...

Suppose S is a finite generalized quadrangle (GQ) of order (s, t), s 6= 1 6= t, and suppose that L is a line of S. A symmetry about L is an automorphism of the GQ which fixes every line of S meeting L (including L). A line is called an axis of symmetry if there is a full group of symmetries of size s about this line, and a point of a generalized quadrangle is a translation point if every line t...

We give a characterization of translation ovoids of flock generalized quadrangles. Then we prove that, if q = 2e , each elation generalized quadrangle defined by a flock has a large class of translation ovoids which arise from semifields of dimension two over their left nucleus. Finally, we give some examples when q is odd. © 2003 Elsevier Ltd. All rights reserved. MSC (2000): Primary 51E12; Se...

 This paper discusses models for manufacturing systems that are based on generalized stochastic Petri nets and on Markov decision processes. We employ generalized stochastic Petri nets to model manufacturing processes with high degree of uncertainty due to the human operator behavior. We extend the usual generalized stochastic Petri nets by allowing imprecision about probabilities to be explic...