We obtain asymptotic for the quantity $\int_0^1 \bigg|\sum_{n\le X}\tau_k(n)e(n\alpha)\bigg|d\alpha$ where $\tau_k(n) = \sum_{d_1\dots d_k n} 1$. This follows from a quick application of circle method. Along way, we find minor arc bounds exponential sum with $\tau_k$, and asymptotics high moments Dirichlet kernel.

We study two topologies $ \tau_{KR} and \tau_K on the space of measures a completely regular generated by Kantorovich–Rubinshtein Kantorovich seminorms analogous to their classical norms in case metric space. The topology coincides with weak nonnegative bounded uniformly tight sets measures. A sufficient condition is given for compactness topology. show that logarithmically concave measures, so...

This paper is concerned with the problem of best weighted simultaneous approximations to totally bounded sequences in Banach spaces. Characterization results from convex sets in Banach spaces are established under the assumption that the Banach space is uniformly smooth.

In this paper, we continue to study convergence problems for a Ishikawa-like iterative process for a finite family of m-accretive mappings. Strong convergence theorems are established in uniformly smooth Banach spaces.

Absolutely representing system (ARS) in a Banach space X is a set D ⊂ X such that every vector x in X admits a representation by an absolutely convergent series x = ∑ i aixi with (ai) ⊂ R and (xi) ⊂ D. We investigate some general properties of ARS. In particular, ARS in uniformly smooth and in B-convex Banach spaces are characterized via ε-nets of the unit balls. Every ARS in a B-convex Banach ...