Related papers: Anti M-Weierstrass function sequences

We propose a unified framework for establishing existence of nonparametric M-estimators, computing the corresponding estimates, and proving their strong consistency when the class of functions is exceptionally rich. In particular, the…

A further significant extension is presented of the infinitely large class of differential algebras of generalized functions which are the basic structures in the nonlinear algebraic theory listed under 46F30 in the AMS Mathematical Subject…

We consider the space of real-valued continuously differentiable functions on a compact subset of a euclidean space. We characterize the completeness of this space and prove that the space of restrictions of continuously differentiable…

When dealing with concrete problems in a function space on R^n, it is sometimes helpful to have a dense subspace consisting of functions of a particular type, adapted to the problem under consideration. We give a theorem that allows one to…

Let $m,n$ be positive integers. In this short note we prove that the set of all continuous and surjective functions from $\mathbb{R}^{m}$ to $\mathbb{R}^{n}$ contains (excluding the 0 function) a $\mathfrak{c}$-dimensional vector space.…

Fractional difference sequence spaces have been studied in the literature recently. In this work, some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain operators on some difference…

We show that every finite-dimensional Euclidean space contains compact universal differentiability sets of upper Minkowski dimension one. In other words, there are compact sets $S$ of upper Minkowski dimension one such that every Lipschitz…

In a wide class of weighted Bergman spaces, we construct invertible non-cyclic elements. These are then used to produce z-invariant subspaces of index higher than one. In addition, these elements generate nontrivial bilaterally invariant…

The most important uniform algebra is the family of continuous functions on a compact subset $K$ of the complex plane $\mathbb{C}$ which are analytic on the interior int$(K)$ For compact sets $K$ which are regular (i.e. $K =$int$(K)$ and…

We determine the Weierstrass semigroup at one and two totally ramified places in a Kummer extension defined by the affine equation $y^{m}=\prod_{i=1}^{r} (x-\alpha_i)^{\lambda_i}$ over $K$, the algebraic closure of $\mathbb{F}_q$, where…

The $\alpha$-Weierstrass function is defined as $W_g^{\alpha,b}(x) = \sum_{k=0}^{\infty} b^{-\alpha k} g(b^k x)$, where $g$ is a Lipschitz function on the unit circle. For a prevalent $\alpha$-Weierstrass function, we prove that the upper…

A topological description of various generalized function algebras over corresponding basic locally convex algebras is given. The framework consists of algebras of sequences with appropriate ultra(pseudo)metrics defined by sequences of…

We show that a subspace $S$ of the space of real analytical functions on a manifold that satisfies certain regularity properties is contained in the set of solutions of a linear elliptic differential equation. The regularity properties are…

It is shown that quasi all continuous functions on the unit circle have the property that, for many small subsets E of the circle, the partial sums of their Fourier series considered as functions restricted to E exhibit certain universality…

It is proved that each of compact linear groups of one special type admits a semialgebraic continuous factorization map onto a real vector space.

Finite topological spaces are in bijective correspondence with preorders on finite sets. We undertake their study using combinatorial tools that have been developed to investigate general discrete structures. A particular emphasis will be…

Directed spaces are natural topological extensions of dcpos in domain theory and form a cartesian closed category. In order to model nondeterministic semantics, the power structures over directed spaces were defined through the form of free…

Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…

Main results of the paper: (1) For any finite metric space $M$ the Lipschitz free space on $M$ contains a large well-complemented subspace which is close to $\ell_1^n$. (2) Lipschitz free spaces on large classes of recursively defined…

In a metric space, such as the real numbers with their standard metric, a set A is open if and only if no sequence with terms outside of A has a limit inside A. Moreover, a metric space is compact if and only if every sequence has a…