Related papers: Strongly Cesaro type quasi-Cauchy sequences

It is well known that there is an integral theorem for quaternion-valued functions analogous to Cauchys Theorem for complex-valued functions, namely Fueters Theorem. The class of quaternionic functions for which this applies are generally…

The connection between symmetries and conservation laws as made by Noether's theorem is extended to the context of causal variational principles and causal fermion systems. Different notions of continuous symmetries are introduced. It is…

We establish a Fenchel-Moreau type theorem for proper convex functions $f\colon X\to \bar{L}^0$, where $(X, Y, \langle \cdot,\cdot \rangle)$ is a dual pair of Banach spaces and $\bar L^0$ is the space of all extended real-valued functions…

We study real-valued, continuous and translation invariant valuations defined on the space of quasi-concave functions of N variables. In particular, we prove a homogeneous decomposition theorem of McMullen type, and we find a representation…

We give necessary and sufficient conditions for a real-valued quasiconvex function f on a Baire topological vector space X (in particular, Banach or Frechet space) to be continuous at the points of a residual subset of X. These conditions…

The main result of this paper is a proof of the continuity of a family of integral functionals defined on the space of functions of bounded variation with respect to a topology under which smooth functions are dense. These functionals occur…

This paper is a continuation of work started in \cite{njampavcont} on preserving continuity in ideal topological spaces. We will deal with $\theta$-continuity and weak continuity and give their translations in ideal topological spaces. As…

We introduce a notion of quasiconvexity for continuous functions $f$ defined on the vector bundle of linear maps between the tangent spaces of a smooth Riemannian manifold $(M,g)$ and $\mathbb{R}^m$, naturally generalizing the classical…

We prove that for each locally $\alpha$-presentable category $\mathcal K$ there exists a regular cardinal $\gamma$ such that any $\alpha$-accessible functor out of $\mathcal K$ (into another locally $\alpha$-presentable category) is…

Many definitions of weak and strict $\infty$-categories have been proposed. In this paper we present a definition for $\infty$-categories with strict associators, but which is otherwise fully weak. Our approach is based on the existing type…

We investigate strongly symmetric homeomorphisms of the real line which appear in harmonic analysis aspects of quasiconformal Teichm\"uller theory. An element in this class can be characterized by a property that it can be extended…

We do three things in this paper: (1) study the analog of localization sequences (in the sense of algebraic $K$-theory of stable $\infty$-categories) for additive $\infty$-categories, (2) define the notion of nilpotent extensions for…

The main result of this paper is a quantified version of Ingham's Tauberian theorem for bounded vector-valued sequences rather than functions. It gives an estimate on the rate of decay of such a sequence in terms of the behaviour of a…

Let $\Omega $ be a bounded ${\mathcal{C}}^{\infty}$-smoothly bounded domain in ${\mathbb{C}}^{n}.$ For such a domain we define a new notion between strict pseudo-convexity and pseudo-convexity: the size of the set $W$ of weakly…

For an inner function $\theta$ on the unit disk, let $K^p_\theta:=H^p\cap\theta\overline{H^p_0}$ be the associated star-invariant subspace of the Hardy space $H^p$. While the squaring operation $f\mapsto f^2$ maps $H^p$ into $H^{p/2}$, one…

Let $\Delta_m$ be the standard $m$-dimensional simplex of non-negative $m+1$ tuples that sum to unity and let $S$ be a nonempty subset of $\Delta_m$. A real valued function $h$ defined on a convex subset of a real vector space is $S$-almost…

We construct various examples of Sobolev-type functions, defined via upper gradients in metric spaces, that fail to be quasicontinuous or weakly quasicontinuous. This is done with quasi-Banach function lattices $X$ as the function spaces…

We introduce the notion of {\it approximation type} for the partial, and in certain cases the total description of extensions of a given valuation from a field $K$ to the rational function field $K(x)$. To every extension, a unique…

We show weak lower semi-continuity of functionals assuming the new notion of a "convexly constrained" $\mathcal A$-quasiconvex integrand. We assume $\mathcal A$-quasiconvexity only for functions defined on a set $K$ which is convex.…

The space of constructible functions form a dense subspace of the space of generalized valuations. In this note we prove a somewhat stronger property that the sequential closure, taken sufficiently many (in fact, infinitely many) times, of…