Christoffel functions and Tura´n determinants on several intervals

@article{Assche1993ChristoffelFA,
  title={Christoffel functions and Tura´n determinants on several intervals},
  author={Walter Van Assche},
  journal={Journal of Computational and Applied Mathematics},
  year={1993},
  volume={48},
  pages={207-223}
}
  • W. Assche
  • Published 29 October 1993
  • Mathematics
  • Journal of Computational and Applied Mathematics
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15 Citations
Background Citations
3
Methods Citations
1

15 Citations

Christoffel functions for multiple orthogonal polynomials
. We study weak asymptotic behaviour of the Christoffel–Darboux kernel on the main diagonal corresponding to multiple orthogonal polynomials. We show that under some hypotheses the weak limit of 1 𝑛…
Asymptotic behavior of Christoffel-Darboux kernel via three-term recurrence relation II
Asymptotic Behaviour of Orthogonal Polynomials on the Unit Circle with Asymptotically Periodic Reflection Coefficients: II. Weak Asymptotics☆☆☆
Abstract In this paper we study orthogonal polynomials with asymptotically periodic reflection coefficients. It's known that the support of the orthogonality measure of such polynomials consists of…
Regular Article: The Christoffel Function for Orthogonal Polynomials on a Circular Arc
For the special type of weight functions on circular arc we study the asymptotic behavior of the Christoffel kernel off the arc and of the Christoffel function inside the arc. We prove Totik's…
Asymptotic Behaviour of Christoffel–Darboux Kernel Via Three-Term Recurrence Relation I
For Jacobi parameters belonging to one of three classes: asymptotically periodic, periodically modulated, and the blend of these two, we study the asymptotic behavior of the Christoffel functions and…
Discrete Spectrum of the Jacobi Matrix Related to Recurrence Relations with Periodic Coefficients
In this note, we study the discrete spectrum of the Jacobi matrix corresponding to polynomials defined by recurrence relations with periodic coefficients. As examples, we consider(a) the case where…
Periodic perturbations of unbounded Jacobi matrices II: Formulas for density
Asymptotics for Christoffel functions for general measures on the real line
We consider asymptotics of Christoffel functions for measures ν with compact support on the real line. It is shown that under some natural conditionsn times thenth Christoffel function has a limit…
Trace Formula for Orthogonal Polynomials with Asymptotically 2-Periodic Recurrence Coefficients
where an+1=kn kn+1>0 and bn # R. Conversely, by Favard's Theorem, if the polynomials pn(x) are given by the recurrence formula (1.1) with an+1>0 and bn # R, then there exists a positive Boreal…
Christoffel functions and finite moment problems
The Christoffel functions are used here to approximate an unknown probability density u:(0,1) to R+ whose first m moments mu 1,..., mu m only are available. We obtain a sequence u(m) of estimators…
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References

SHOWING 1-10 OF 15 REFERENCES
Approximating the weight function for orthogonal polynomials on several intervals
Asymptotics for Orthogonal Polynomials and Three-Term Recurrences
It is often desirable to obtain (asymptotic) properties of orthogonal polynomials and the measure with respect to which these polynomials are orthogonal. All orthogonal polynomials on the real line…
ASYMPTOTIC PROPERTIES OF POLYNOMIALS ORTHOGONAL ON A SYSTEM OF CONTOURS, AND PERIODIC MOTIONS OF TODA LATTICES
An expression in the form of a Riemann theta-function is obtained for the asymptotic behavior of polynomials orthogonal on a system of contours. Properties of a limit-periodic discrete…
Orthogonal polynomials with asymptotically periodic 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…
Sieved ultraspherical polynomials
The continuous q-ultraspherical polynomials contain a number of important examples as limiting or special cases. One of these arose in Allaway's Ph.D. thesis. In a previous paper we solved a…
ORTHOGONAL POLYNOMIALS ON SEVERAL INTERVALS VIA A POLYNOMIAL MAPPING
Starting from a sequence {pn{x; no)} of orthogonal polynomials with an orthogonality measure yurj supported on Eo C (—1,1), we construct a new sequence {p"(x;fi)} of orthogonal polynomials on£ =…
Orthogonal Polynomials, Recurrences, Jacobi Matrices, and Measures
This is a compact bare bone survey of some aspects of orthogonal polynomials addressed primarily to nonspecialists. Special attention is paid to characterization theorems and to spectral properties…
Ge´za Freud, orthogonal polynomials and Christoffel functions. A case study
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.
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