in this paper, we first introduce some function spaces, with certain locally convex topologies, closely  related to the space of real-valued continuous functions on $x$,  where $x$ is a $c$-distinguished topological space. then, we show that their dual spaces can be identified in a natural way with certain spaces of radon measures.

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...

Abstract We investigate random minimal factorizations of the n -cycle, that is, permutation $(1 \, 2 \cdots n)$ into a product cycles $\tau_1, \ldots, \tau_k$ whose lengths $\ell(\tau_1), \ell(\tau_k)$ satisfy minimality condition $\sum_{i=1}^k(\ell(\tau_i)-1)=n-1$ . By associating to cycle factorization black polygon inscribed in unit disk, and reading one after another, we code by process col...

We prove strong convergence theorem for infinite family of uniformly L−Lipschitzian total quasi-φ-asymptotically nonexpansive multi-valued mappings using a generalized f−projection operator in a real uniformly convex and uniformly smooth Banach space. The result presented in this paper improve and unify important recent results announced by many authors.

In this paper, we first introduce some function spaces, with certain locally convex topologies, closely  related to the space of real-valued continuous functions on $X$,  where $X$ is a $C$-distinguished topological space. Then, we show that their dual spaces can be identified in a natural way with certain spaces of Radon measures.

In general, the Gelfand widths cn(T ) of a map T between Banach spaces X and Y are not equivalent to the Gelfand numbers cn(T ) of T . We show that cn(T ) = cn(T ) (n ∈ N) provided that X and Y are uniformly convex and uniformly smooth, and T has trivial kernel and dense range. c ⃝ 2012 Elsevier Inc. All rights reserved.

Article history: Received 2 April 2014 Available online 2 July 2014 Submitted by P. Nevai

Almost transitive superreflexive Banach spaces have been considered in [7] (see also [4] and [6]), where it is shown that such spaces are uniformly convex and uniformly smooth. We prove that convex transitive Banach spaces are either almost transitive and superreflexive (hence uniformly smooth) or extremely rough. The extreme roughness of a Banach space X means that, for every element u in the ...