2016
DOI: 10.1016/j.jmaa.2016.02.012
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On a class of biorthogonal polynomials on the unit circle

Abstract: A system of biorthogonal polynomials with respect to a complex valued measure supported on the unit circle is considered and all the terms with bounds are explicitly given for the remainder of an asymptotic formula given by R. Askey for this system. An electrostatic interpretation for the zeros of a class of para-orthogonal polynomials associated with the biorthogonal system is also considered.

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Cited by 4 publications
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“…Let us also record that special cases of the Askey polynomials were obtained in [22] as Fourier transforms of Laguerre polynomials (with weights attached). We refer to [23] for historical remarks regarding these polynomials (see also [4]).…”
Section: Introductionmentioning
confidence: 99%
“…Let us also record that special cases of the Askey polynomials were obtained in [22] as Fourier transforms of Laguerre polynomials (with weights attached). We refer to [23] for historical remarks regarding these polynomials (see also [4]).…”
Section: Introductionmentioning
confidence: 99%
“…Let us also record that special cases of the Askey polynomials were obtained in [5] as Fourier transforms of Laguerre polynomials (with weights attached). We refer to [6] for historical remarks regarding these polynomials (see also [7]).…”
Section: Introductionmentioning
confidence: 99%
“…For this measure, the Verblunsky coefficients satisfy α M −1 = ζ and α n = 0 for n = M − 1 (see 1 [28, page 84]). Again, for the sake of clarity, we will specialise to the case of ζ = 1/2 and derive the second order ODE for Φ n (z; β).…”
mentioning
confidence: 99%
“…Acknowledgments. We would like to thank Mihai Stoiciu for much useful conversation and also Andrei Martinez-Finkelshtein for useful feedback on this work and for bringing the paper [1] to our attention. We would also like to thank the anonymous referee for directing us to the observation that Theorem 1.2 can be applied even if |β| = 1.…”
mentioning
confidence: 99%