Prediction of weakly stationary sequences on polynomial hypergroups

Prediction of Weakly Stationary Sequences on Polynomial Hypergroups

HOMOMORPHISMS OF l-ALGEBRAS ON SIGNED POLYNOMIAL HYPERGROUPS

Let {Rn} and {Pn} be two polynomial systems which induce signed polynomial hypergroup structures on N0. We investigate when the Banach algebra l(N0, h) can be continuously embedded into or is isomorphic to l(N0, h ). We find sufficient conditions on the connection coefficients cnk given by Rn = ∑n k=0 cnkPk, for the existence of such an embedding or isomorphism. Finally we apply these results t...

Point Derivations on the l-Algebra of Polynomial Hypergroups

Polynomial hypergroups are a very interesting class of hypergroups with a great variety of examples which are quite different from groups. So the L-algebras of hypergroups have properties very distinguished to the L-algebras of groups, in particular in the context of amenability and related conditions. Being amenable the L-algebra of an abelian group does not possess any non-zero bounded point ...

Prediction and Nongaussian Autoregressive Stationary Sequences

The object of this paper is to show that under certain auxiliary assumptions a stationary autoregressive sequence has a best predictor in mean square that is linear if and only if the sequence is minimum phase or is Gaussian when all moments are finite.

Ergodic sequences of probability measures on commutative hypergroups

We study conditions on a sequence of probability measures {µ n } n on a commutative hyper-group K, which ensure that, for any representation π of K on a Hilbert space Ᏼ π and for any ξ ∈ Ᏼ π , (K π x (ξ)dµ n (x)) n converges to a π-invariant member of Ᏼ π. 1. Introduction. The mean ergodic theorem was originally formulated by von Neu-mann [13] for one-parameter unitary groups in Hilbert space. ...