begin{abstract} In this paper, we introduce an iterative method for amenable semigroup of non expansive mappings and infinite family of non expansive mappings in the frame work of Hilbert spaces. We prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. The results present...

Multipliers of reproducing kernel Hilbert spaces can be characterized in terms positivity $n \times n$ matrices analogous to the classical Pick matrix. We study for which it suffices consider bounded size $n$. connect this problem notion subhomogeneity non-selfadjoint operator algebras. Our main results show that multiplier algebras many analytic functions, such as Dirichlet space and Drury-Arv...

Solutions to the Riemann-Hilbert problems with irregular singularities naturally associated to semisimple Frobenius manifold structures on Hurwitz spaces (moduli spaces of meromorphic functions on Riemann surfaces) are constructed. The solutions are given in terms of meromorphic bidifferentials defined on the underlying Riemann surface. The relationship between different classes of Frobenius ma...

In the paper we find, for certain values of the parameters, the spaces of multipliers ( H(p, q, α), H(s, t, β) ) and ( H(p, q, α), ls ) , where H(p, q, α) denotes the space of analytic functions on the unit disc such that (1 − r)Mp(f, r) ∈ Lq( dr 1−r ). As corollaries we recover some new results about multipliers on Bergman spaces and Hardy spaces. §0. Introduction. Given two sequence spaces X ...

We study multivariate L2-approximation for a weighted Korobov space of analytic periodic functions for which the Fourier coefficients decay exponentially fast. The weights are defined, in particular, in terms of two sequences a = {aj} and b = {bj} of positive real numbers bounded away from zero. We study the minimal worst-case error eL2−app,Λ(n, s) of all algorithms that use n information evalu...