Error Bounds of Gaussian Quadratures for One Class of Bernstein-Szego Weight Functions

We consider the action of the automorphism group I(n) of Zn on the set of k−sets of Zn in the natural way. Although elementary in its nature, it has not been fully analyzed and understood yet. The vast class of enumerative and computational problems problems is related to this action. For example, the number of orbits on the set of k−sets of Zn is one of them that we are interested in. Those enumerative problems are mainly resolved by application of P olya's theory

Iterates of maps which are non-expansive in Hilbert's projective metric

summary:The cycle time of an operator on $R^n$ gives information about the long term behaviour of its iterates. We generalise this notion to operators on symmetric cones. We show that these cones, endowed with either Hilbert’s projective metric or Thompson’s metric, satisfy Busemann’s definition of a space of non- positive curvature. We then deduce that, on a strictly convex symmetric cone, the cycle time exists for all maps which are non-expansive in both these metrics. We also review an analogue for the Hilbert metric of the Denjoy-Wolff theorem

PSA 2020

These preprints were automatically compiled into a PDF from the collection of papers deposited in PhilSci-Archive in conjunction with the PSA 2020