Best one-sided approximation of convolution classes by cardinal splines

Let G be a Polya frequency density and its periodization. We get the exact value of upper approximation of S₁ (G), which is a convolution class with kernel G, by cardinal splines corresponding to G. Similar result has been obtained for periodic convolution class with kernel as well. Supported in part by Postdoctral Fellowship Foundation provided by Chinese Academy of Sciences     

An exponent bound on skew Hadamard abelian difference sets

A difference setD in a groupG is called a skew Hadamard difference set (or an antisymmetric difference set) if and only ifG is the disjoint union ofD, D(^–1), and {1}, whereD(^–1)={d^–1|dD}. In this note, we obtain an exponent bound for non-elementary abelian groupG which admits a skew Hadamard difference set. This improves the bound obtained previously by Johnsen, Camion and Mann.