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Diego Dominici

Publications and source records attributed to Diego Dominici.

At least 19 recordsLinked to original sources
arXiv2025

Asymptotic analysis of a family of Sobolev orthogonal polynomials related to the generalized Charlier polynomials

In this paper we tackle the asymptotic behavior of a family of orthogonal polynomials with respect to a nonstandard inner product involving the forward operator Δ. Concretely, we treat the generalized Charlier weights in the framework of Δ--Sobolev orthogonality. We obtain an asymptotic expansion for this orthogonal polynomials where the falling factorial polynomials play an important role.

math.CA↗
arXiv2023

Symmetrization process and truncated orthogonal polynomials

We define the family of truncated Laguerre polynomials $P_n(x;z)$, orthogonal with respect to the linear functional $\ell$ defined by $$\langle{\ell,p\rangle}=\int_{0}^zp(x)x^αe^{-x}dx,\qquadα>-1.$$ The connection between $P_n(x;z)$ and the polynomials $S_n(x;z)$ (obtained through the symmetrization process) constitutes a key element in our analysis. As a consequence, several properties of the polynomials $P_n(x;z)$ and $S_n(x;z)$ are studied taking into account the relation between the parameters of the three-term recurrence relations that they satisfy. Asymptotic expansions of these coefficients are given. Discrete Painlevé and Painlevé equations associated with such coefficients appear in a natural way. An electrostatic interpretation of the zeros of such polynomials as well as the dynamics of the zeros in terms of the parameter $z$ are given.

math.CA↗
arXiv2022

Truncated Hermite polynomials

We consider the family of polynomials $p_{n}\left( x;z\right) ,$ orthogonal with respect to the inner product \[ \left\langle f,g\right\rangle = \int_{-z}^{z} f\left( x\right) g\left( x\right) e^{-x^{2}} \,dx. \] We show some properties about the coefficients in their 3-term recurrence relation, connections between $p_{n}\left( x;z\right) $ and $p_{n}^{\prime}\left( x;z\right) ,$ a second order differential equation satisfied by $p_{n}\left( x;z\right) ,$ and an electrostatic interpretation of their zeros.

math.CA↗
arXiv2020

Orthogonality of the Dickson polynomials of the (k+1)-th kind

We study the Dickson polynomials of the (k+1)-th kind over the field of complex numbers. We show that they are a family of co-recursive orthogonal polynomials with respect to a quasi-definite moment functional L_{k}. We find an integral representation for L_{k} and compute explicit expressions for all of its moments.

math.CA↗
arXiv2019

Discrete semiclassical orthogonal polynomials of class 2

In this contribution, discrete semiclassical orthogonal polynomials of class $s\leq2$ are studied. By considering all possible solutions of the Pearson equation, we obtain the canonical families in each class. We also consider limit relations between these and other families of orthogonal polynomials.

math.CA↗
arXiv2014

Mehler-Heine type formulas for Charlier and Meixner polynomials

We derive Mehler--Heine type asymptotic formulas for Charlier and Meixner polynomials, and also for their associated families. These formulas provide good approximations for the polynomials in the neighborhood of $x=0,$ and determine the asymptotic limit of their zeros as the degree $n$ goes to infinity.

math.CA↗
arXiv2012

Discrete semiclassical orthogonal polynomials of class one

We study the discrete semiclassical orthogonal polynomials of class s=1. By considering all possible solutions of the Pearson equation, we obtain five canonical families. We also consider limit relations between these and other families of orthogonal polynomials.

math.CA↗
arXiv2012

Asymptotic analysis of nested derivatives

We analyze the nested derivatives of a function $\mathfrak{D}^{n}[f]\,(x)$ asymptotically, as $n\rightarrow\infty,$ using a discrete version of the ray method. We give some examples showing the accuracy of our formulas.

math.CA↗
arXiv2009

An Arithmetic Metric

What is the distance between 11 (a prime number) and 12 (a highly composite number)? If your answer is 1, then ask yourself "is this reasonable?" In this work, we will introduce a distance between natural numbers based on their arithmetic properties, instead of their position on the real line.

math.NT↗
arXiv2009

Polynomial solutions of differential-difference equations

We investigate the zeros of polynomial solutions to the differential-difference equation \[ P_{n+1}(x)=A_{n}(x)P_{n}^{\prime}(x)+B_{n}(x)P_{n}(x), n=0,1,... \] where $A_{n}$ and $B_{n}$ are polynomials of degree at most 2 and 1 respectively. We address the question of when the zeros are real and simple and whether the zeros of polynomials of adjacent degree are interlacing. Our result holds for general classes of polynomials but includes sequences of classical orthogonal polynomials as well as Euler-Frobenius, Bell and other polynomials.

math.CA↗
arXiv2008

Asymptotic analysis of a family of polynomials associated with the inverse error function

We analyze the sequence of polynomials defined by the differential-difference equation $P_{n+1}(x)=P_{n}^{\prime}(x)+x(n+1)P_{n}(x)$ asymptotically as $n\to\infty$. The polynomials $P_{n}(x)$ arise in the computation of higher derivatives of the inverse error function $\operatorname{inverf}(x)$. We use singularity analysis and discrete versions of the WKB and ray methods and give numerical results showing the accuracy of our formulas.

math.CA↗
arXiv2008

Polynomial solutions of nonlinear integral equations

We analyze the polynomial solutions of a nonlinear integral equation, generalizing the work of C. Bender and E. Ben-Naim. We show that, in some cases, an orthogonal solution exists and we give its general form in terms of kernel polynomials.

math.CA↗
arXiv2008

Asymptotic analysis of a fluid model modulated by an $M/M/1$ queue

We analyze asymptotically a differential-difference equation, that arises in a Markov-modulated fluid model. We use singular perturbation methods to analyze the problem with appropriate scalings of the two state variables. In particular, the ray method and asymptotic matching are used.

math.PR↗