Related papers: Continuous functions on Berkovich spaces

The purpose of this paper is to show that Non-Archimedean Mathematics (NAM), namely mathematics which uses infinite and infinitesimal numbers, is useful to model some Physical problems which cannot be described by the usual mathematics. The…

Given some non-Archimedean field $\mathbb{K}$ and some $\mathbb{K}$-linear space $X$, the usual way to define a norm over $X$ involves the {\em ultrametric inequality} $\|x+y\|\leq\max\{\|x\|,\|y\|\}$. In this note we will try to analyse…

We present here an analogue of the Brian\c{c}on-Skoda theorem for a germ of an analytic space $Z$ at 0, such that $O_{Z,0}$ is Cohen-Macaulay, but not necessarily reduced. More precisely, we find a sufficient condition for membership of a…

Let $\omega=[a_1, a_2, \cdots]$ be the infinite expansion of continued fraction for an irrational number $\omega \in (0,1)$; let $R_n (\omega)$ (resp. $R_{n, \, k} (\omega)$, $R_{n, \, k+} (\omega)$) be the number of distinct partial…

We introduce the notion of Dunkl completely monotonic functions on $\left(-\sigma,\sigma\right), \sigma>0$. We establish a restrictive version of the analogue of Schoenberg's theorem in Dunkl setting.

Given a bounded open set $\Omega\subset \mathbb{R}^n$, we study sequences of quadratic functionals on the Sobolev space $H^1_0(\Omega)$, perturbed by sequences of bounded linear functionals. We prove that their $\Gamma$-limits, in the weak…

We formulate a multi-valued version of the Tietze-Urysohn extension theorem. Precisely, we prove that any upper semicontinuous multi-valued map with nonempty closed convex values defined on a closed subset (resp. closed perfectly normal…

We study varieties of certain ordered $\Sigma$-algebras with restricted completeness and continuity properties. We give a general characterization of their free algebras in terms of submonads of the monad of $\Sigma$-coterms. Varieties of…

Let B be a p-uniformly convex Banach space, with p >= 2. Let T be a linear operator on B, and let A_n x denote the ergodic average (1 / n) sum_{i< n} T^n x. We prove the following variational inequality in the case where T is power bounded…

This article explores anti-coproximinal and strongly anti-coproximinal subspaces in the spaces of vector-valued continuous functions and operator spaces. We provide a complete characterization of strongly anti-coproximinal subspaces in $…

We establish nontrivial bounds for general bilinear forms with a given periodic function, which are thought of as an analogue of van der Corput differencing for exponential sums. The proof employs Poisson summation, Cauchy-Schwarz, and the…

Let $k$ be an algebraically closed complete non-Archimedean field, and let $K$ be a finitely generated field extension over $k$ with transcendence degree $1$. Equip $K$ a non-Archimedean norm extending the one on $k$, and let $\mathcal{K}$…

We consider convex sets and functions over idempotent semifields, like the max-plus semifield. We show that if $K$ is a conditionally complete idempotent semifield, with completion $\bar{K}$, a convex function $K^n\to\bar{K}$ which is lower…

Let X be a separable Banach space which admits a separating polynomial; in particular X a separable Hilbert space. Let $f:X \rightarrow R$ be bounded, Lipschitz, and $C^1$ with uniformly continuous derivative. Then for each {\epsilon}>0,…

Let $|\cdot|$ be the standard Euclidean norm on $\mathbb{R}^n$ and let $X=(\mathbb{R}^n,\|\cdot\|)$ be a normed space. A subspace $Y\subset X$ is \emph{strongly $\alpha$-Euclidean} if there is a constant $t$ such that…

Extended real-valued functions are often used in optimization theory, but in different ways for infimum problems and for supremum problems. We present an approach to extended real-valued functions that works for all types of problems and…

We obtain a uniform ergodic theorem for the sequence $\frac1{s(n)} \sum_{k=0}^n(\varDelta s)(n-k)\,T^k$, where $\varDelta$ is the inverse of the endomorphism on the vector space of scalar sequences which maps each sequence into the sequence…

As is well known absolute convergence and unconditional convergence for series are equivalent only in finite dimensional Banach spaces. Replacing the classical notion of absolutely summing operators by the notion of 1 summing operators \[…

The concept of angle, angle functions, and the question how to measure angles present old and well-established mathematical topics referring to Euclidean space, and there exist also various extensions to non-Euclidean spaces of different…

Quasi-invariant and pseudo-differentiable measures on a Banach space $X$ over a non-Archimedean locally compact infinite field with a non-trivial valuation are defined and constructed. Measures are considered with values in $\bf R$.…