Geodesic
Mixed Type Hermite--Pad\'e Approximants for a Nikishin System
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analysis and mathematical physics, Tome 311 (2020), pp. 213-227

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We consider the problem of mixed type Hermite–Padé approximants and prove that the Nikishin system is perfect for this problem. Using the method of a vector equilibrium problem, we find weak asymptotics and prove the convergence of the approximants along any rays in the index table. We also present an equivalent statement in the form of a matrix Riemann–Hilbert problem.
Keywords: mixed type Hermite–Padé approximants, Nikishin system, perfect system, vector logarithmic-potential equilibrium problem, matrix Riemann–Hilbert problem.
Mots-clés : convergence of rational approximants 
@article{TM_2020_311_a11,
     author = {V. G. Lysov},
     title = {Mixed {Type} {Hermite--Pad\'e} {Approximants} for a {Nikishin} {System}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {213--227},
     publisher = {mathdoc},
     volume = {311},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2020_311_a11/}
}
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V. G. Lysov. Mixed Type Hermite--Pad\'e Approximants for a Nikishin System. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analysis and mathematical physics, Tome 311 (2020), pp. 213-227. http://geodesic.mathdoc.fr/item/TM_2020_311_a11/