Browsing by Subject "Bergman orthogonal polynomials"
Now showing items 1-7 of 7
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Asymptotics for Hessenberg Matrices for the Bergman Shift Operator on Jordan Regions
(2014)Let G be a bounded Jordan domain in the complex plane. The Bergman polynomials {pn}n=0∞ of G are the orthonormal polynomials with respect to the area measure over G. They are uniquely defined by the entries of an infinite ...
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Bergman Orthogonal Polynomials and the Grunsky Matrix
(2017)By exploiting a link between Bergman orthogonal polynomials and the Grunsky matrix, probably first observed by Kühnau (Ann Acad Sci Math 10:313–329, 1985), we improve on some recent results on strong asymptotics of Bergman ...
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Bergman polynomials on an archipelago: Estimates, zeros and shape reconstruction
(2009)Growth estimates of complex orthogonal polynomials with respect to the area measure supported by a disjoint union of planar Jordan domains (called, in short, an archipelago) are obtained by a combination of methods of ...
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Error analysis of the Bergman kernel method with singular basis functions
(2011)Let G be a bounded Jordan domain in the complex plane with a piecewise analytic boundary. We present theoretical estimates and numerical evidence for certain phenomena, regarding the application of the Bergman kernel method ...
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On finite-term recurrence relations for Bergman and Szego{double acute} polynomials
(2012)With the aid of Havin's Lemma (which we generalize) we prove that polynomials orthogonal over the unit disk with respect to certain weighted area measures (Bergman polynomials) cannot satisfy a finite-term recurrence ...
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Strong Asymptotics for Bergman Polynomials over Domains with Corners and Applications
(2013)Let G be a bounded simply-connected domain in the complex plane ℂ, whose boundary Γ {colon equals} ∂G is a Jordan curve, and let {pn}n=0 ∞denote the sequence of Bergman polynomials of G. This is defined as the unique ...
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Article
Zero distribution of Bergman orthogonal polynomials for certain planar domains
(2003)Let G be a simply connected domain in the complex plane bounded by a closed Jordan curve L and let Pn, n ≥ 0, be polynomials of respective degrees n = 0, 1,... that are orthonormal in G with respect to the area measure ...