Alexander R. Its, Leon A. Takhtajan
Published 2007-08-28Version 1
We 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.
On the norms and roots of orthogonal polynomials in the plane and $L^p$-optimal polynomials with respect to varying weights
Some Orthogonal Polynomials in Four Variables
Riemann-Hilbert Methods in the Theory of Orthogonal Polynomials
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