Szegő Difference Equations, Transfer Matrices¶and Orthogonal Polynomials on the Unit Circle

Golinskiĭ, Leonid; Nevai, Paul

doi:10.1007/s002200100525

Cited by 77 publications

(81 citation statements)

References 2 publications

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“…We note that the control of oscillatory solutions only under (4.1) is subtle, using ideas of Kooman [36]; see also Golinskii-Nevai [37] and Section 12.1 of [2].…”

Section: This Results Includes Results Of Vertesimentioning

confidence: 99%

Fine Structure of the Zeros of Orthogonal Polynomials: A Review

Simon

2007

Difference Equations, Special Functions and Orthogonal Polynomials

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Mhaskar-Saff found a kind of universal behavior for the bulk structure of the zeros of orthogonal polynomials for large n. Motivated by two plots, we look at the finer structure for the case of random Verblunsky coefficients and for what we call the BLS condition: α n = Cb n + O((b∆) n ). In the former case, we describe results of Stoiciu. In the latter case, we prove asymptotically equal spacing for the bulk of zeros.

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“…We note that the control of oscillatory solutions only under (4.1) is subtle, using ideas of Kooman [36]; see also Golinskii-Nevai [37] and Section 12.1 of [2].…”

Section: This Results Includes Results Of Vertesimentioning

confidence: 99%

Fine Structure of the Zeros of Orthogonal Polynomials: A Review

Simon

2007

Difference Equations, Special Functions and Orthogonal Polynomials

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“…This connection have been actively studied during the last decades. See, for instance, [1]- [5], [12,25] and numerous references therein. The connections between block Toeplitz matrices and Weyl theory for the self-adjoint discrete Dirac system were treated in [11].…”

Section: Introductionmentioning

confidence: 99%

On a new class of structured matrices related to the discrete skew-self-adjoint Dirac systems

Fritzsche¹,

Kirstein²,

Sakhnovich³

2008

ELA

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Abstract.A new class of the structured matrices related to the discrete skew-self-adjoint Dirac systems is introduced. The corresponding matrix identities and inversion procedure are treated. Analogs of the Schur coefficients and of the Christoffel-Darboux formula are studied. It is shown that the structured matrices from this class are always positive-definite, and applications for an inverse problem for the discrete skew-self-adjoint Dirac system are obtained.

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“…In particular, we note the following result of Golinskii-Nevai [8]: Theorem 1.5 If V 0 = 0, V is decaying, and for some q ∈ N,…”

Section: Introductionmentioning

confidence: 99%

Destruction of Absolutely Continuous Spectrum by Perturbation Potentials of Bounded Variation

Last

2007

Commun. Math. Phys.

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Szegő Difference Equations, Transfer Matrices¶and Orthogonal Polynomials on the Unit Circle

Cited by 77 publications

References 2 publications

Fine Structure of the Zeros of Orthogonal Polynomials: A Review

Fine Structure of the Zeros of Orthogonal Polynomials: A Review

On a new class of structured matrices related to the discrete skew-self-adjoint Dirac systems

Destruction of Absolutely Continuous Spectrum by Perturbation Potentials of Bounded Variation

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