Related papers: Mellin Analysis and its distance concept. Applicat…
The notions of distance and similarity play a key role in many machine learning approaches, and artificial intelligence (AI) in general, since they can serve as an organizing principle by which individuals classify objects, form concepts…
Here we give a new approach to the Paley--Wiener theorem in a Mellin analysis setting which avoids the use of the Riemann surface of the logarithm and analytical branches and is based on new concepts of "polar-analytic function" in the…
Mellin transform is used to evaluate an integral involving the product of four Bessel functions and a power. Using this method the result is obtained in terms of generalized hypergeometric functions $_{6}F_{5}$.
We apply the techniques of computable model theory to the distance function of a graph. This task leads us to adapt the definitions of several truth-table reducibilities so that they apply to functions as well as to sets, and we prove…
We propose a fractional variant of Mellin's transform which may find an application in the Conformal Field Theory. Its advantage is the presence of an arbitrary parameter which may substantially simplify calculations and help adjusting…
We define a Mellin amplitude for CFT$_1$ four-point functions. Its analytical properties are inferred from physical requirements on the correlator. We discuss the analytic continuation that is necessary for a fully nonperturbative…
Making use of inverse Mellin transform techniques for analytical continuation, an elegant proof and an extension of the zeta function regularization theorem is obtained. No series commutations are involved in the procedure; nevertheless the…
Within the framework of algebraic quantum field theory a general method is presented which allows one to compute and classify the short distance (scaling) limit of any algebra of local observables. The results can be used to determine the…
The concepts of similarity and distance are crucial in data mining. We consider the problem of defining the distance between two data sets by comparing summary statistics computed from the data sets. The initial definition of our distance…
The notion of supershift (in itself a generalization of the notion of superoscillation arising in quantum mechanics) expresses the fact that the sampling of a function in an interval allows to compute the values of the function far from the…
For a functional defined on the class of closed one-dimensional connected subsets of ${\mathbb R}^n$ we consider the corresponding minimization problem and we give suitable first order necessary conditions of optimality. The cases studied…
We construct a Lipschitz truncation which approximates functions of bounded variation in the area-strict metric. The Lipschitz truncation changes the original function only on a small set similar to Lusin's theorem. Previous results could…
In this paper, we present a novel interpretation of the so-called Weisfeiler-Lehman (WL) distance, introduced by Chen et al. (2022), using concepts from stochastic processes. The WL distance aims at comparing graphs with node features, has…
In a recent work I showed that the family of smooth steep time functions can be used to recover the order, the topology and the (Lorentz-Finsler) distance of spacetime. In this work I present the main ideas entering the proof of the…
We apply the Mellin-Barnes integral representation to several situations of interest in mathematical-physics. At the purely mathematical level, we derive useful asymptotic expansions of different zeta-functions and partition functions.…
In this paper, we continue the study of the polar analytic functions, a notion introduced in \cite{BBMS1} and successfully applied in Mellin analysis. Here we obtain another version of the Cauchy integral formula and a residue theorem for…
We study the space of bandlimited Lipschitz functions in one variable. In particular we provide a geometrical description of the natural interpolating and sampling sequences for this space. We also find a description of the trace of such…
In this paper we study Hankel operators in the quaternionic setting. In particular we prove that they can be exploited to measure the $L^{\infty}$ distance of a slice $L^{\infty}$ function from the space of bounded slice regular functions.
This paper presents a distance function between sets based on an average of distances between their elements. The distance function is a metric if the sets are non-empty finite subsets of a metric space. It can be applied to produce various…
The Mellin transform is usually applied in probability theory to the product of independent random variables. In recent times the machinery of the Mellin transform has been adopted to describe the L\'evy stable distributions, and more…