Related papers: Positive Definite Distributions and Normed Spaces

We introduce and analyze spaces and algebras of generalized functions which correspond to H\" older, Zygmund, and Sobolev spaces of functions. The main scope of the paper is the characterization of the regularity of distributions that are…

We show that the problem whether a given finite metric space can be embedded into $m$-dimensional rectilinear space can be reformulated in terms of the Gromov--Hausdorff distance between some special finite metric spaces.

Definition. A symmetric with respect to 0 bounded closed convex set A in a finite dimensional normed space X is called a sufficient enlargement for X (or of B(X)) if for arbitrary isometric embedding of X into a Banach space Y there exists…

We discuss some finite homogeneous structures, addressing the question of universality of their automorphism groups. We also study the existence of so-called Kat\v{e}tov functors in finite categories of embeddings or homomorphisms.

We prove that every proper $n$-dimensional length metric space admits an "approximate isometric embedding" into Lorentzian space $\mathbb{R}^{3n+6,1}$. By an "approximate isometric embedding" we mean an embedding which preserves the energy…

We endow the set of complements of a fixed subspace of a projective space with the structure of an affine space, and show that certain lines of such an affine space are affine reguli or cones over affine reguli. Moreover, we apply our…

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

In this paper we parallelly build up the theories of normed linear spaces and of linear spaces with indefinite metric, called also Minkowski spaces for finite dimensions in the literature. In the first part of this paper we collect the…

We study the asymptotic behaviour of the approximation, Gelfand and Kolmogorov numbers of the compact embeddings of weighted function spaces of Besov and Triebel-Lizorkin type in the case where the weights belong to a large class. We obtain…

We are concerned with the well-posedness of linear elliptic systems posed on $\mathbb{R}^d$. The concrete problem of interest, for which we require this theory, arises from the linearization of the equations of anisotropic finite…

We define distribution spaces of a sequence of convolutions of a set of distributions with smooth functions, the shearlet system. Then, we define associated sequence spaces and prove characterizations. We also show a reproducing identity in…

A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed…

In this paper we generalize Kaplansky's combinatorial characterization of the isomorphism types of embeddings of a cyclic subgroup in a finite abelian group given in his 1951 book ``Infinite Abelian Groups''. For this we introduce partial…

We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.

We find a new finite algorithm for evaluation of Lipschitz-free $p$-space norm in finite-dimensional Lipschitz-free $p$-spaces. We use this algorithm to deal with the problem of whether given $p$-metric spaces $N\subset M$, the canonical…

We apply a symmetrization procedure to the setting of Jacobi expansions and study potential spaces in the resulting situation. We prove that the potential spaces of integer orders are isomorphic to suitably defined Sobolev spaces. Among…

We consider the space of complete and separable metric spaces which are equipped with a probability measure. A notion of convergence is given based on the philosophy that a sequence of metric measure spaces converges if and only if all…

The problem of classification of cubic homogeneous Finslerian 3D metrics with respect to their isometries is considered. It is shown, that there are 6 different general affine types of such metrics. Algebras of isometries are presented in…

We consider a general notion of snowflake of a metric space by composing the distance by a nontrivial concave function. We prove that a snowflake of a metric space $X$ isometrically embeds into some finite-dimensional normed space if and…

Gromov \cite{Gr$_1$} and Dranishnikov \cite{Dr$_1$} introduced asymptotic and coarse dimensions of proper metric spaces via quite different ways. We define coarse and asymptotic dimension of all metric spaces in a unified manner and we…