اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدDistribution of points of interpolation and of zeros of exact maximally convergent multipoint Pade approximants
126
0
0.0
(
0
)
تأليف
R. K. Kovacheva
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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.
قيم البحث
اقرأ أيضاً
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 He
rmite-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.
In the paper, we propose two new conjectures about the convergence of Hermite Approximants of multivalued analytic functions of Laguerre class ${mathscr L}$. The conjectures are based in part on the numerical experiments, made recently by the authors in [26] and [27].
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 approxima
nts). 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.
A well known result due to Carlson affirms that a power series with finite and positive radius of convergence R has no Ostrowski gaps if and only if the sequence of zeros of its nth sections is asymptotically equidistributed to {|z|=R}. Here we exten
d this characterization to those power series with null radius of convergence, modulo some necessary normalizations of the sequence of the sections of f.
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), r
esp. 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.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
