Exact Bounds for orthogonal polynomials associated with exponential weights

Nevai, Paul

doi:10.1016/0021-9045(85)90070-x

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2023

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Cited by 24 publications

(3 citation statements)

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“…In [16], strong (C, 1) means of orthonormal expansions for Erdo s weights were investigated; there for p= , instead of 9 n in (22) there was a factor T &1Â4 in the left-hand side. Since one can show that…”

Section: Introduction and Resultsmentioning

confidence: 99%

(C, 1) Means of Orthonormal Expansions for Exponential Weights

Lubinsky

Mache

2000

Journal of Approximation Theory

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Section: Introduction and Resultsmentioning

confidence: 99%

(C, 1) Means of Orthonormal Expansions for Exponential Weights

Lubinsky

Mache

2000

Journal of Approximation Theory

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“…As Szegö's book indicates, there is a long interesting history of estimates for Hermite, Laguerre and other orthogonal polynomials (see for example [14], [21] and the paper of Erdelyi [18]). For later developments see [33] and the references there. Inequalities (48) imply that…”

Section: Example Spacesmentioning

confidence: 99%

Eigensystem of an L 2-perturbed harmonic oscillator is an unconditional basis

Adduci

Mityagin

2012

Open Mathematics

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We prove the following. For any complex valued L p -function b(x), 2 ≤ p < ∞ or L ∞ -function with the norm b|L ∞ < 1, the spectrum of a perturbed harmonic oscillator operator L = −d 2 /dx 2 + x 2 + b(x) in L 2 (R 1 ) is discrete and eventually simple. Its SEAF (system of eigen-and associated functions) is an unconditional basis in L 2 (R).2000 Mathematics Subject Classification. 47E05, 34L40, 34L10.

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“…x n (x n+1 + x n + x n−1 + K) = αn, α > 0 with x 0 = 0, has a unique positive solution (Lew and Quarles [7], Nevai [8]). This was extended to a more general recurrence relation by Alsulami et al [1].…”

Section: Introductionmentioning

confidence: 99%

Unique special solution for discrete Painlevé II

Van Assche

2023

Journal of Difference Equations and Applications

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We show that the discrete Painlevé II equation with starting value a −1 = −1 has a unique solution for which −1 < a n < 1 for every n ≥ 0. This solution corresponds to the Verblunsky coefficients of a family of orthogonal polynomials on the unit circle. This result was already proved for certain values of the parameter in the equation and recently a full proof was given by Duits and Holcomb [3]. In the present paper we give a different proof that is based on an idea put forward by Tomas Lasic Latimer [6] which uses orthogonal polynomials. We also give an upper bound for this special solution.

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Exact Bounds for orthogonal polynomials associated with exponential weights

Cited by 24 publications

References 13 publications

(C, 1) Means of Orthonormal Expansions for Exponential Weights

(C, 1) Means of Orthonormal Expansions for Exponential Weights

Eigensystem of an L 2-perturbed harmonic oscillator is an unconditional basis

Unique special solution for discrete Painlevé II

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