Related papers: Approximate smoothness in normed linear spaces

For a big class of smooth dagger spaces --- dagger spaces are 'rigid spaces with overconvergent structure sheaf' --- we prove finite dimensionality of de Rham cohomology. This is enough to obtain finiteness of Berthelot's rigid cohomology…

For an arbitrary normed space $\mathcal X$ over a field $\mathbb F \in \{ \mathbb R, \mathbb C \}$, we define the directed graph $\Gamma(\mathcal X)$ induced by Birkhoff-James orthogonality on the projective space $\mathbb P(\mathcal X)$,…

Numerical solutions of differential equations are usually not smooth functions. However, they should resemble the smoothness of the corresponding real solutions in one way or another. In two of our recent papers, a kind of spacial…

In a countably normed space which is a linear space equipped with a countable number of pair-wise compatible norms, we prove the existence of a common nearest point (in all norms) from a point outside a nonempty subset if this subset is…

In this paper, we prove the rate of approximation for the Neural Network Sampling Operators activated by sigmoidal functions with mixed Lebesgue norm in terms of averaged modulus of smoothness for a bounded measurable functions on bounded…

Variable Muckenhoupt weights are considered in variable exponent Lebesgue spaces. Applications are given for polynomial approximation in these spaces. Boundedness of averaging operator is proved to gain a transference result. Almost all…

We study the structure of the space of coarse Lipschitz maps between Banach spaces. In particular we introduce the notion of norm attaining coarse Lipschitz maps. We extend to the case of norm attaining coarse Lipschitz equivalences, a…

We examine the necessary and sufficient complexity of neural networks to approximate functions from different smoothness spaces under the restriction of encodable network weights. Based on an entropy argument, we start by proving lower…

We propose and study quantitative measures of smoothness which are adapted to anisotropic features such as edges in images or shocks in PDE's. These quantities govern the rate of approximation by adaptive finite elements, when no constraint…

We prove a rigidity theorem that shows that, under many circumstances, quasi-isometric embeddings of equal rank, higher rank symmetric spaces are close to isometric embeddings. We also produce some surprising examples of quasi-isometric…

In this paper we study some geometric properties like parallelism, orthogonality and semi-rotundity in the space of bounded linear operators. We completely characterize parallelism of two compact linear operators between normed linear…

In this paper, we introduce cone normed linear space, study the cone convergence with respect to cone norm. Finally, we prove the completeness of a finite dimensional cone normed linear space.

Some sharp discrete inequalities in normed linear spaces are obtained. New reverses of the generalised triangle inequality are also given.

In this paper, we will discuss the notion of almost orthogonality in a functional sequence.Especially, we will define a few sequences of almost orthogonal polynomials which can be used successfully for modeling of electronic systems which…

Given a smooth curve $\gamma$ in some $m$-dimensional surface $M$ in $\mathbb{R}^{m+1}$, we study existence and uniqueness of a flat surface $H$ having the same field of normal vectors as $M$ along $\gamma$, which we call a flat…

Recently, the theory of symmetric spaces has come to play an increased role in the physics of integrable systems and in quantum transport problems. In addition, it provides a classification of random matrix theories. In this paper we give a…

We study the relation between the linear stability of almost-symmetries and the geometry of the Banach spaces on which these transformations are defined. We show that any transformation between finite dimensional Banach spaces that…

We classify the metric spaces that can be approximated by finite homogeneous ones.

We introduce and study the notion of orthosymmetric spaces over an Archimedean vector lattice as a generalization of finite-dimentional Euclidean inner spaces. A special attention has been paid to linear operators on these spaces.

We introduce certain linear positive operators and study some approximation properties of these operators in the space of functions, continuous on a compact set, of two variables. We also find the order of this approximation by using…