Some asymptotic properties for orthogonal polynomials with respect to varying measures
نویسندگان
چکیده
منابع مشابه
Orthogonal polynomials with respect to varying weights 1
In this paper we review a connection of orthogonal polynomials with respect to varying weights to weighted approximation, multipoint Pad6 approximation and to some questions of theoretical physics. (~) 1998 Elsevier Science B.V. All rights reserved.
متن کاملRemarks on Orthogonal Polynomials with Respect to Varying Measures and Related Problems
We point out the relation between the orthogonal polynomials with respect to (w.r.t.) varying measures and the so-called orthogonal rationals on the unit circle in the complex plane. This observation enables us to combine different techniques in the study of these polynomials and rationals. As an example, we present a simple and short proof for a known result on the weak-star convergence of ort...
متن کاملOn Orthogonal Polynomials with Respect to Varying Measures on the Unit Circle
Let {4>„{dfi)} be a system of orthonormal polynomials on the unit circle with respect to d/i and {y/„,m(dß)} be a system of orthonormal polynomials on the unit circle with respect to the varying measures dß/\wn(z)\2, z = e'e , where {w„(z)} is a sequence of polynomials, degw« = n , whose zeros w„ i, ... , wn,n lie in \z\ < 1 The asymptotic behavior of the ratio of the two systems on and outside...
متن کاملRatio and relative asymptotics of polynomials orthogonal with respect to varying Denisov-type measures
Let be a finite positive Borel measure with compact support consisting of an interval [c, d] ⊂ R plus a set of isolated points in R\[c, d], such that ′> 0 almost everywhere on [c, d]. Let {w2n}, n ∈ Z+, be a sequence of polynomials, degw2n 2n, with real coefficients whose zeros lie outside the smallest interval containing the support of . We prove ratio and relative asymptotics of sequences of ...
متن کاملOrthogonal Polynomials with Respect to Self-Similar Measures
We study experimentally systems of orthogonal polynomials with respect to self-similar measures. When the support of the measure is a Cantor set, we observe some interesting properties of the polynomials, both on the Cantor set and in the gaps of the Cantor set. We introduce an effective method to visualize the graph of a function on a Cantor set. We suggest a new perspective, based on the theo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2005
ISSN: 0021-9045
DOI: 10.1016/j.jat.2005.03.002