In this paper, we introduce periodically correlated space-time autoregressive processes with values in Hilbert spaces. The existence conditions and the strong law of large numbers are established. Moreover, present an estimator for autocorrelation parameter such processes.

Moreau’s decomposition is a powerful nonlinear hilbertian analysis tool that has been used in various areas of optimization and applied mathematics. In this paper, it is extended to reflexive Banach spaces and in the context of generalized proximity measures. This extension unifies and significantly improves upon existing results.

We show that there exists a separable reflexive Banach space into which every separable uniformly convex Banach space isomorphically embeds. This solves a problem of J. Bourgain. We also give intrinsic characterizations of separable reflexive Banach spaces which embed into a reflexive space with a block q-Hilbertian and/or a block p-Besselian finite dimensional decomposition.

Abstract From any two median spaces $X$ and $Y$ , we construct a new space $X \circledast Y$ referred to as the diadem product of show that this construction is compatible with wreath products in following sense: given finitely generated groups $G,\,H$ (equivariant) coarse embeddings into $X,\,Y$ there exist a(n equivariant) embedding $G\wr H \to X . The offers unified point view on various que...

Abstract. This paper studies a random walk based on random transvections in SLn(Fq,) and shows that, given 6 > 0, there is a constant c such that after n + c steps the walk is within a distance e from uniform and that after nc steps the walk is a distance at least 1 e from uniform. This paper uses results of Diaconis and Shahshahani to get the upper bound, uses results of Rudvalis to get the lo...