Remarks on E. A. Rahmanov's paper “on the asymptotics of the ratio of orthogonal polynomials”

@article{Mt1982RemarksOE,
  title={Remarks on E. A. Rahmanov's paper “on the asymptotics of the ratio of orthogonal polynomials”},
  author={Attila M{\'a}t{\'e} and Paul Nevai},
  journal={Journal of Approximation Theory},
  year={1982},
  volume={36},
  pages={64-72}
}
  • A. Máté, P. Nevai
  • Published 1 September 1982
  • Mathematics
  • Journal of Approximation Theory
View via Publisher
doi.org
101 Citations
Highly Influential Citations
5
Background Citations
38
Methods Citations
4
Results Citations
2

101 Citations

Perturbations of orthogonal polynomials with periodic recursion coefficients
The results of Denisov-Rakhmanov, Szegő-Shohat-Nevai, and Killip-Simon are extended from asymptotically constant orthogonal polynomials on the real line (OPRL) and unit circle (OPUC) to…
Asymptotics of Orthogonal Polynomials With a Generalized Szeg}o Condition
We focus on the pointwise asymptotics inside the unit disk for orthogonal polynomials with respect to a measure from polynomial Szeg}o class and perturbed by a sequence of point masses outside the…
A new approach to ratio asymptotics for orthogonal polynomials
We use a non-linear characterization of orthonormal polynomials due to Saff in order to prove an equivalence of norm asymptotics and strong asymptotics for polynomials. Several applications of this…
On Rakhmanov's theorem for Jacobi matrices
We prove Rakhmanov's theorem for Jacobi matrices without the additional assumption that the number of bound states is finite. This result solves one of Nevai's open problems.
Christoffel functions and Tura´n determinants on several intervals
The Moment Problem
  • A. Gut
  • Mathematics
    Encyclopedia of Special Functions: The Askey-Bateman Project
  • 2020
The purpose of this paper is to provide some additional insight into the moment problem by connecting a condition by Lin, Bondesson's class of hyperbolically completely monotone densities, and the…
Denisov's theorem on recurrence coefficients
Asymptotics for the ratio of leading coefficients of orthonormal polynomials on the unit circle
Consider a system {φn} of polynomials orthonormal on the unit circle with respect to a measuredμ, withμ′>0 almost everywhere. Denoting bykn the leading coefficient ofφn, a simple new proof is given…
Orthogonal polynomials on the unit circle: New results
We announce numerous new results in the theory of orthogonal polynomials on the unit circle, most of which involve the connection between a measure on the unit circle in the complex plane and the…
functions and Tur&n determinants intervals
Van Assche, W., Christoffel functions and Turan determinants on several intervals, Journal of Computational and Applied Mathematics 48 (1993) 207-223. We consider orthogonal polynomials on the real…
...
...

References

SHOWING 1-4 OF 4 REFERENCES
ON STEKLOV'S CONJECTURE IN THE THEORY OF ORTHOGONAL POLYNOMIALS
This paper constructs an example of a weight function on the interval such that 0$ SRC=http://ej.iop.org/images/0025-5734/36/4/A07/tex_sm_1864_img3.gif/>, , whereas the corresponding sequence of…
On the Asymptotics of the Ratio of Orthogonal Polynomials. Ii
Let be a positive measure on the circumference and let almost everywhere on . Let be the orthogonal polynomials corresponding to , and let be their parameters. Then .Bibliography: 5 titles.
Convergence of Diagonal PADÉ Approximants
Let be a positive measure with compact support contained in , and set This paper studies the convergence of diagonal Pade approximants for meromorphic functions of the form , where is a rational…
On asymptotic properties of polynomials which are orthogonal on the unit circle, and on certain properties of positive harmonic functions