Related papers: Mellin Analysis and its distance concept. Applicat…
The main purpose of this paper is to apply the theory of vector lattices and the related abstract modular convergence to the context of Mellin-type kernels and (non)linear vector lattice-valued operators, following the construction of an…
The aim of the present article is to give an introduction to the concept of quasi-unitary equivalence and to define several (pseudo-)metrics on the space of self-adjoint operators acting possibly in different Hilbert spaces. As some of the…
Motivated by the problem of constructing bijective maps with low differential uniformity, we introduce the notion of permutation resemblance of a function, which looks to measure the distance a given map is from being a permutation. We…
The paper establishes a functional version of the Hoeffding combinatorial central limit theorem. First, a pre-limiting Gaussian process approximation is defined, and is shown to be at a distance of the order of the Lyapounov ratio from the…
In general, while obtaining the probability density function of sums and products of shifted random variables, ordinary analytical methods such as Fourier and Mellin transforms tend to provide integrals which cannot be expressed in terms of…
The paper deals with (multidimensional and one-dimensional) Bochner-Phillips functional calculus. Bounded perturbations of Bernstein functions of (one or several commuting) semigroup generators on Banach spaces are considered, conditions…
We have derived some new results for the Mellin transform formulas, as well as for the Gauss hypergeometric function. Also, we have found the connection between the Legendre functions of the second kind. Some of the results obtained we used…
In a recent paper, a "distance" function, \cal D, was defined which measures the distance between pure classical and quantum systems. In this work, we present a new definition of a "distance", D, which measures the distance between either…
We propose an alternative to $k$-nearest neighbors for functional data whereby the approximating neighboring curves are piecewise functions built from a functional sample. Using a locally defined distance function that satisfies…
In this work we establish a theory of Calculus based on the new concept of displacement. We develop all the concepts and results necessary to go from the definition to differential equations, starting with topology and measure and moving on…
The Bregman divergence (Bregman distance, Bregman measure of distance) is a certain useful substitute for a distance, obtained from a well-chosen function (the "Bregman function"). Bregman functions and divergences have been extensively…
A common way to quantify the ,,distance'' between measures is via their discrepancy, also known as maximum mean discrepancy (MMD). Discrepancies are related to Sinkhorn divergences $S_\varepsilon$ with appropriate cost functions as…
Classical machine learning approaches are sensitive to non-stationarity. Transfer learning can address non-stationarity by sharing knowledge from one system to another, however, in areas like machine prognostics and defense, data is…
We show that on separable Banach spaces admitting a separating polynomial, any uniformly continuous, bounded, real-valued function can be uniformly approximated by Lipschitz, analytic maps on bounded sets.
Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…
This paper studies approximation properties of linear sampling operators in general Banach lattices $X$. We obtain matching direct and inverse approximation estimates, convergence criteria, equivalence results involving special…
In this paper we develop an algebraic theory to study the problem of finding the minimum distance point from an algebraic variety with respect to the Hermitian distance function. The theory generalizes the Euclidean Distance degree…
Recently D. Buchholz and R. Verch have proposed a method for implementing in algebraic quantum field theory ideas from renormalization group analysis of short-distance (high energy) behavior by passing to certain scaling limit theories.…
This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain…
In generalized Lebesgue spaces L^{p(.)} with variable exponent p(.) defined on the real axis, we obtain several inequalities of approximation by integral functions of finite degree. Approximation properties of Bernstein singular integrals…