2025/01/01 by Sergey Pavlovich Suetin
Computer Science · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Polynomial and algebraic computation #Quantum chaos and dynamical systems
paper · pdf · doi:10.4213/rm10194e
crossref issued 2025/01/01 · crossref published 2025/01/01 · crossref published-print 2025/01/01 · openalex publication_date 2025/01/01 · crossref published-online 2025/04/30 · crossref created 2025/05/01 · crossref deposited 2025/05/01 · openalex created_date 2025/10/10 · crossref indexed 2026/07/27 · openalex updated_date 2026/07/27
The problem of the existence of a limit distribution of the zeros of Hermite-Padé polynomials for a pair of functions forming a Nikishin system is discussed. Two new scalar methods are proposed for the investigation of this problem. The first is based on a potential-theoretic equilibrium problem stated on a two-sheeted Riemann surface and on the use of the Gonchar-Rakhmanov-Stahl (GRS-)method in treating this problem. The second method is based on the existence of a three-sheeted Riemann surface with Nuttall partition into sheets which is associated with a given pair of functions f, f2, and it uses only the maximum principle for subharmonic functions. The connection of these methods and the results obtained with Stahl's methods and results of 1987-88 is discussed. Results of numerical experiments are presented. Bibliography: 109 titles.