Related papers: Interpolating function and Stokes Phenomena
We consider the problem of uniform interpolation of functions with values in a complex inner product space of finite dimension. This problem can be casted within a modified weighted pluripotential theoretic framework. Indeed, in the…
In the present work, the notion of Super Fractal Interpolation Function (SFIF) is introduced for finer simulation of the objects of the nature or outcomes of scientific experiments that reveal one or more structures embedded in to another.…
Rational inner functions are a generalization of finite Blaschke products to several variables. In this article we survey a variety of results about rational inner functions related to interpolation, sums of squares formulas, and boundary…
We study the structure of the flat space wavefunctional in scalar field theories with nonlinearly realized symmetries. These symmetries imply soft theorems that are satisfied by wavefunction coefficients in the limit where one of the…
A method is described for the extrapolation of perturbative expansions in powers of asymptotically small coupling parameters or other variables onto the region of finite variables and even to the variables tending to infinity. The method…
Let X be a countably infinite set of real numbers and let Y_x, x \in X, be an independent family of stationary random subsets of the real numbers, e.g. homogeneous Poisson point processes. We give criteria for the a.s. existence of various…
The problem of extrapolating asymptotic perturbation-theory expansions in powers of a small variable to large values of the variable tending to infinity is investigated. The analysis is based on self-similar approximation theory. Several…
We propose new universal formulae for thermal two-point functions of scalar operators based on their analytic structure, constructed to manifestly satisfy all the bootstrap conditions. We derive a dispersion relation in the complexified…
We characterize interpolating sequences for multiplier algebras of spaces with the complete Pick property. Specifically, we show that a sequence is interpolating if and only if it is separated and generates a Carleson measure. This…
Reconstruction of density functions and their characteristic functions by radial basis functions with scattered data points is a popular topic in the theory of pricing of basket options. Such functions are usually entire or admit an…
We study schemes for interpolating functions that take values in the special orthogonal group $SO(n)$. Our focus is on interpolation schemes obtained by embedding $SO(n)$ in a linear space, interpolating in the linear space, and mapping the…
Structure functions are the essential objects for understanding the deep inelastic scattering processes, providing valuable insight into the partonic structure of hadrons. A direct calculation of the Compton amplitude provides a…
Histopolation, or interpolation on segments, is a mathematical technique used to approximate a function $f$ over a given interval $I=[a,b]$ by exploiting integral information over a set of subintervals of $I$. Unlike classical polynomial…
We study various properties of $f$-divergences and Csisz\'ar indices between two probability distributions in very general setups for the convex function $f$ and for the probability distributions. We establish general structural properties…
A method is suggested for interpolating between small-variable and large-variable asymptotic expansions. The method is based on self-similar approximation theory resulting in self-similar root approximants. The latter are more general than…
The method of Fractional Borel Summation is suggested in conjunction with self-similar factor approximants. The method used for extrapolating asymptotic expansions at small variables to large variables, including the variables tending to…
Disordered and frustrated graphical systems are ubiquitous in physics, biology, and information science. For models on complete graphs or random graphs, deep understanding has been achieved through the mean-field replica and cavity methods.…
For a series of Markov processes we prove stochastic duality relations with duality functions given by orthogonal polynomials. This means that expectations with respect to the original process (which evolves the variable of the orthogonal…
Motivated by polynomial approximations of differential forms, we study analytical and numerical properties of a polynomial interpolation problem that relies on function averages over interval segments. The usage of segment data gives rise…
We reduce the computation of three point function of three spinning operators with arbitrary polarizations to a statistical mechanics problem via the hexagon formalism. The central building block of these correlation functions is the…