Related papers: Interpolating function and Stokes Phenomena

In this present paper, I propose a derivation of unified interpolation and extrapolation function that predicts new values inside and outside the given range by expanding direct Taylor series on the middle point of given data set.…

Interpolating functional method is a powerful tool for studying the behavior of a quantity in the intermediate region of the parameter space of interest by using its perturbative expansions at both ends. Recently several interpolating…

In this paper, we study functional approximations where we choose the so-called radial basis function method and more specifically, quasi-interpolation. From the various available approaches to the latter, we form new quasi-Lagrange…

We investigate geometric aspects of co-equational parametric resurgence, by studying physical problems whose formal asymptotic solutions give rise to Borel transforms lying on an algebraic curve. This perspective allows us to elucidate…

We study inverse factorial series and their relation to Stirling numbers of the first kind. We prove a special representation of the polylogarithm function in terms of series with such numbers. Using various identities for Stirling numbers…

In these notes we give an overview of different topics in resurgence theory from a physics point of view, but with particular mathematical flavour. After a short review of the standard Borel method for the resummation of asymptotic series,…

We construct a large family of Fourier interpolation bases for functions analytic in a strip symmetric about the real line. Interesting examples involve the nontrivial zeros of the Riemann zeta function and other $L$-functions. We establish…

Interpolation of classes of differentiated functions given on a finite interval by trigonometric splines using the phantom node method is considered. This method consists in supplementing a given sequence of values of an approximate…

We discuss non-commutative field theories in coordinate space. To do so we introduce pseudo-localized operators that represent interesting position dependent (gauge invariant) observables. The formalism may be applied to arbitrary field…

The higher-order Stokes phenomenon can emerge in the asymptotic analysis of many problems governed by singular perturbations. Indeed, over the last two decades, the phenomena has appeared in many physical applications, from acoustic and…

We provide a rigorous study on dimensions of fractal interpolation function defined on a closed and bounded interval of $\mathbb{R}$ which is associated to a continuous function with respect to a base function, scaling functions and a…

The theory of resurgence uniquely associates a factorially divergent formal power series with a collection of exponentially small non-perturbative corrections paired with a set of complex numbers known as Stokes constants. When the Borel…

The quantum dilogarithm function of Faddeev is a special function that plays a key role as the building block of quantum invariants of knots and 3-manifolds, of quantum Teichm\"uller theory and of complex Chern-Simons theory. Motivated by…

We study the Stokes phenomenon for the solutions of the 1-dimensional complex heat equation and its generalizations with meromorphic initial data. We use the theory of Borel summability for the description of the Stokes lines, the…

High-dimensional/high-fidelity nonlinear dynamical systems appear naturally when the goal is to accurately model real-world phenomena. Many physical properties are thereby encoded in the internal differential structure of these resulting…

We consider eigenvalue problems in quantum mechanics in one dimension. Hamiltonians contain a class of double well potential terms, x^6 + \alpha x^2, for example . The space coordinate is continued to a complex plane and the connection…

Dimension theory lies at the heart of fractal geometry and concerns the rigorous quantification of how large a subset of a metric space is. There are many notions of dimension to consider, and part of the richness of the subject is in…

Fractal interpolation technique is an alternative to the classical interpolation methods especially when a chaotic signal is involved. The logic behind the formulation of an iterated function system for the construction of fractal…

Given a sequence of real numbers, we consider its subsequences converging to possibly different limits and associate to each of them an index of convergence which depends on the density of the associated subsequences. This index turns out…

In this paper we consider interpolation in model spaces, $H^2 \ominus B H^2$ with $B$ a Blaschke product. We study unions of interpolating sequences for two sequences that are far from each other in the pseudohyperbolic metric as well as…