Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn overconvergent subsequencs of closed to rows classical Pade approximants
101
0
0.0
(
0
)
Authors
Ralitza K. Kovacheva
Ask ChatGPT about the research
No Arabic abstract
Let $f$ be a power series with positive radius of convergence. In the present paper, we study the phenomenon of overconvergence of sequences of classical Pade approximants pi{n,m_n} associated with f, where m(n)<=m(n+1)<=m(n) and m(n) = o(n/log n), resp. m(n) = 0(n) as n is going to infiity. We extend classical results by J. Hadamard and A. A. Ostrowski related to overconvergent Taylor polynomials, as well as results by G. Lopez Lagomasino and A. Fernandes Infante concerning overconvergent subsequences of a fixed row of the Pade table.
rate research
Read More
Starting from the orthogonal polynomial expansion of a function $F$ corresponding to a finite positive Borel measure with infinite compact support, we study the asymptotic behavior of certain associated rational functions (Pad{e}-orthogonal approximants). We obtain both direct and inverse results relating the convergence of the poles of the approximants and the singularities of $F.$ Thereby, we obtain analogues of the theorems of E. Fabry, R. de Montessus de Ballore, V.I. Buslaev, and S.P. Suetin.
Given a vector function ${bf F}=(F_1,ldots,F_d),$ analytic on a neighborhood of some compact subset $E$ of the complex plane with simply connected complement, we define a sequence of vector rational functions with common denominator in terms of the expansions of the components $F_k, k=1,ldots,d,$ with respect to the sequence of Faber polynomials associated with $E$. Such sequences of vector rational functions are analogous to row sequences of type II Hermite-Pade approximation. We give necessary and sufficient conditions for the convergence with geometric rate of the common denominators of the sequence of vector rational functions so constructed. The exact rate of convergence of these denominators is provided and the rate of convergence of the approximants is estimated. It is shown that the common denominators of the approximants detect the poles of the system of functions closest to $E$ and their order.
Given a system of functions f = (f1, . . . , fd) analytic on a neighborhood of some compact subset E of the complex plane, we give necessary and sufficient conditions for the convergence with geometric rate of the common denominators of multipoint Hermite-Pade approximants. The exact rate of convergence of these denominators and of the approximants themselves is given in terms of the analytic properties of the system of functions. These results allow to detect the location of the poles of the system of functions which are in some sense closest to E.
Given a regular compact set $E$ in the complex plane, a unit measure $mu$ supported by $partial E,$ a triangular point set $beta := {{beta_{n,k}}_{k=1}^n}_{n=1}^{infty},betasubset partial E$ and a function $f$, holomorphic on $E$, let $pi_{n,m}^{beta,f}$ be the associated multipoint $beta-$ Pade approximant of order $(n,m)$. We show that if the sequence $pi_{n,m}^{beta,f}, ninLambda, m-$ fixed, converges exact maximally to $f$, as $ntoinfty,ninLambda$ inside the maximal domain of $m-$ meromorphic continuability of $f$ relatively to the measure $mu,$ then the points $beta_{n,k}$ are uniformly distributed on $partial E$ with respect to the measure $mu$ as $ ninLambda$. Furthermore, a result about the zeros behavior of the exact maximally convergent sequence $Lambda$ is provided, under the condition that $Lambda$ is dense enough.
Analytic approximations to the ground-state energy of closed-shell quantum dots (number of electrons from 2 to 210) are presented in the form of two-point Pade approximants. These Pade approximants are constructed from the small- and large-density limits of the energy. We estimated that the maximum error, reached for intermediate densities, is less than 3%. Within the present approximation the ground-state is found to be unpolarized.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
