2007/08/28 by Alexander Its, Alexander R. Its, Leon A. Takhtajan +2 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Matrix Theory and Algorithms #Quantum Mechanics and Non-Hermitian Physics #math-ph #math.CA #math.MP #nlin.SI
paper · pdf · doi:10.48550/arxiv.0708.3867
14 pages
arxiv created 2007/08/28 · openalex publication_date 2007/08/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.