Abstract:
We state a new interpolation problem, which we solve using Salikhov's integral. This was previously used in the theory of Diophantine approximations. We study the asymptotic behaviour of orthogonal polynomials related to this problem.
Key words and phrases:
Approximations of logarithms, Hermite–Padé approximations, saddle-point method, algebraic functions and Riemann surfaces, equilibrium logarithmic potentials.
\Bibitem{Sor16}
\by V.~N.~Sorokin
\paper On Salikhov's integral
\serial Tr. Mosk. Mat. Obs.
\yr 2016
\vol 77
\issue 1
\pages 131--154
\publ MCCME
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo585}
\elib{https://elibrary.ru/item.asp?id=28931386}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2016
\vol 77
\pages 107--126
\crossref{https://doi.org/10.1090/mosc/254}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85002398114}
Linking options:
https://www.mathnet.ru/eng/mmo585
https://www.mathnet.ru/eng/mmo/v77/i1/p131
This publication is cited in the following 4 articles:
Alexander Aptekarev, Alexander Dyachenko, Vladimir Lysov, “On Perfectness of Systems of Weights Satisfying Pearson's Equation with Nonstandard Parameters”, Axioms, 12:1 (2023), 89
V. G. Lysov, “Mnogourovnevye interpolyatsii dlya obobschennoi sistemy Nikishina na grafe-dereve”, Tr. MMO, 83, no. 2, MTsNMO, M., 2022, 345–361
V. G. Lysov, “Multilevel interpolations for the generalized Nikishin system on a tree graph”, Trans. Moscow Math. Soc., –
V. G. Lysov, “O diofantovykh priblizheniyakh proizvedeniya logarifmov”, Preprinty IPM im. M. V. Keldysha, 2018, 158, 20 pp.
Citation in format AMSBIB
Contact us: