Géza Freud, orthogonal polynomials and Christoffel functions. A case study

Neval, Paul

doi:10.1016/0021-9045(86)90016-x

Cited by 353 publications

(206 citation statements)

References 239 publications

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“…Moreover, asymptotics for the Christo¤el function n (x) = 1=K n (x; x) have been studied for decades and are reasonably well understood [5], [21], [22], [30].…”

Section: N=0mentioning

confidence: 99%

Universality Limits at the Hard Edge of the Spectrum for Measures with Compact Support

Lubinsky

2010

International Mathematics Research Notices

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“…Moreover, asymptotics for the Christo¤el function n (x) = 1=K n (x; x) have been studied for decades and are reasonably well understood [5], [21], [22], [30].…”

Section: N=0mentioning

confidence: 99%

Universality Limits at the Hard Edge of the Spectrum for Measures with Compact Support

Lubinsky

2010

International Mathematics Research Notices

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“…The methods used to prove the following result for Christo¤el functions are well known for orthogonal polyonomials over intervals and curves [16], [21], [22], [29]. For Bergman polynomials, there are far fewer results [7], [8].…”

Section: Christoffel Functionsmentioning

confidence: 99%

Universality Type Limits for Bergman Orthogonal Polynomials

Lubinsky

2010

Comput. Methods Funct. Theory

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“…[20], [16]). We begin with corollaries which provide exact asymptotics of orthonormal polynomials under stronger assumptions than Theorem 1 and Theorem 2.…”

Section: Convergence Of Christoffel Functionsmentioning

confidence: 99%

Periodic perturbations of unbounded Jacobi matrices II: Formulas for density

Świderski

2017

Journal of Approximation Theory

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Abstract. We give formulas for the density of the measure of orthogonality for orthonormal polynomials with unbounded recurrence coefficients. The formulas involve limits of appropriately scaled Turán determinants or Christoffel functions. Exact asymptotics of the polynomials and numerical examples are also provided. IntroductionConsider a sequence (p n : n ∈ N) of polynomials defined by(1)for sequences a = (a n : n ∈ N) and b = (b n : n ∈ N) satisfying a n > 0 and b n ∈ R. The sequence (1) is orthonormal in L 2 (µ) for a Borel measure µ on the real line. We are interested in the case when the sequence a is unbounded and the measure µ is unique.When it holds, we want to find conditions on the sequences a and b assuring absolute continuity of µ and a constructive formula for its density. In the case when the sequences a and b are bounded, there are several approaches to an approximation of the density of µ. One is obtained by means of N -shifted Turán determinants, i.e. expressions of the formfor positive N (see [19,8,24]). Another by Christoffel functions, i.e.(see [18,23]).2010 Mathematics Subject Classification. Primary: 42C05.

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Géza Freud, orthogonal polynomials and Christoffel functions. A case study

Cited by 353 publications

References 239 publications

Universality Limits at the Hard Edge of the Spectrum for Measures with Compact Support

Universality Limits at the Hard Edge of the Spectrum for Measures with Compact Support

Universality Type Limits for Bergman Orthogonal Polynomials

Periodic perturbations of unbounded Jacobi matrices II: Formulas for density

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