Related papers: Mellin Analysis and its distance concept. Applicat…
Let $G$ be a nonempty bounded domain in a finite-dimensional Euclidean space. The main results are general estimates from below at points from $G$ for an arbitrary subharmonic function $u\not\equiv -\infty$ on the closure of the domain $G$…
The formal term-by-term differentiation with respect to parameters is demonstrated to be legitimate for the Mittag-Leffler type functions. The justification of differentiation formulas is made by using the concept of the uniform…
Distance function to a compact set plays a central role in several areas of computational geometry. Methods that rely on it are robust to the perturbations of the data by the Hausdorff noise, but fail in the presence of outliers. The…
Given a bounded domain, we deal with the problem of estimating the distance function from the internal points of the domain to the boundary of the domain. Convolutional and differential distance estimation schemes are considered and, for…
We consider sequences of additive functionals of difference approximations for uniformly non-degenerate multidimensional diffusions. The conditions are given, sufficient for such a sequence to converge weakly to a W-functional of the…
We study the best approximation and distance problems in the operator space $\B(\HS)$ and in the space of trace class operators $\LS^1(\B(\HS))$. Formulations of distances are obtained in both cases. The case of finite-dimensional…
Given a unital algebra $\mathscr A$ of locally Lipschitz functions defined over a metric measure space $({\mathrm X},{\mathsf d},\mathfrak m)$, we study two associated notions of function of bounded variation and their relations: the space…
The notion of distance between a global Maxwellian function and an arbitrary solution $f$ (with the same total density $\rho$ at the fixed moment $t$) of Boltzmann equation is introduced. In this way we essentially generalize the important…
Discrete partially ordered sets can be turned into distance spaces in several ways. The distance functions may or may not satisfy the triangle inequality, and restriction of the distance to finite chains may or may not coincide with the…
This paper is the first of three in which I study the moduli space of isometry classes of (compact) globally hyperbolic spacetimes (with boundary). I introduce a notion of Gromov-Hausdorff distance which makes this moduli space into a…
We present a definition of the distance between probability distributions. Our definition is based on the $L_1$ norm on space of probability measures. We compare our distance with the well-known Kullback-Leibler divergence and with the…
We provide a general framework to study convergence properties of families of maps. For manifolds $M$ and $N$ where $M$ is equipped with a volume form $\mathcal{V}$ we consider families of maps in the collection $\{(\phi, B) : B \subset M,…
We propose a definition of sampling set for the Nevanlinna class in the disk, i.e. a subset of the disk such that the analogue of the norm of a function in the Nevanlinna class can be recovered only from its values on the subset. We show it…
The difficulties arising in the investigation of finite-size scaling in $d$--dimensional O(n) systems with strong anisotropy and/or long-range interaction, decaying with the interparticle distance $r$ as $r^{-d-\sigma}$ ($0<\sigma\leq2$),…
Probabilistic submeasures generalizing the classical (numerical) submeasures are introduced and discussed in connection with some classes of aggregation functions. A special attention is paid to triangular norm-based probabilistic…
This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra? It turns out that some interesting and simple results can be obtained. These…
A fundamental problem in manifold learning is to approximate a functional relationship in a data chosen randomly from a probability distribution supported on a low dimensional sub-manifold of a high dimensional ambient Euclidean space. The…
A functional distance ${\mathbb H}$, based on the Hausdorff metric between the function hypographs, is proposed for the space ${\mathcal E}$ of non-negative real upper semicontinuous functions on a compact interval. The main goal of the…
We improve the rate function of McDiarmid's inequality for Hamming distance. In particular, applying our result to the separately Lipschitz functions of independent random variables, we also refine the convergence rate function of…
We study the approximation of stationary processes by a simple class of purely deterministic signals. This has an analytic counterpart in the approximation of symmetric positive definite Toeplitz matrices by submatrices of finite rank. We…