Normal matrix models, dbar-problem, and orthogonal polynomials on the complex plane

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dc.creatorIts, Alexander R.
dc.creatorTakhtajan, Leon A.
dc.date2007-08-28
dc.date.accessioned2026-07-07T08:26:19Z
dc.date.available2026-07-07T08:26:19Z
dc.descriptionWe introduce a dbar-formulation of the orthogonal polynomials on the complex plane, and hence of the related normal matrix model, which is expected to play the same role as the Riemann-Hilbert formalism in the theory of orthogonal polynomials on the line and for the related Hermitian model. We propose an analog of Deift-Kriecherbauer-McLaughlin-Venakides-Zhou asymptotic method for the analysis of the relevant dbar-problem, and indicate how familiar steps for the Hermitian model, e.g. the g-function ``undressing'', might look like in the case of the normal model. We use the particular model considered recently by P. Elbau and G. Felder as a case study.
dc.description14 pages
dc.identifierhttps://arxiv.org/abs/0708.3867
dc.identifierhttp://arxiv.org/abs/0708.3867
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/136900
dc.subjectClassical Analysis and ODEs
dc.subjectMathematical Physics
dc.subjectExactly Solvable and Integrable Systems
dc.titleNormal matrix models, dbar-problem, and orthogonal polynomials on the complex plane
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