Geodesic
The analogue of Jacobi's theorem for simultaneous Hermitian interpolation of several functions
Problemy fiziki, matematiki i tehniki, no. 1 (2023), pp. 89-92 Cet article a éte moissonné depuis la source Math-Net.Ru

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The sufficient conditions are found under which rational Hermite – Jacobi approximations exist for a system of functions. It is shown that under these conditions, the Hermite – Jacobi approximations coincide with the corresponding Hermite – Padе approximations. The main result in the particular case when the system consists of one function is well-known Jacobi’s theorem.
Mots-clés : Hadamard determinants, Hermite – Jacobi approximants.
Keywords: perfect systems of functions, Hermite – Padе approximants 
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T. M. Osnach; N. V. Ryabchenko; A. P. Starovoitov. The analogue of Jacobi's theorem for simultaneous Hermitian interpolation of several functions. Problemy fiziki, matematiki i tehniki, no. 1 (2023), pp. 89-92. http://geodesic.mathdoc.fr/item/PFMT_2023_1_a13/

[1] E.M. Nikishin, V.N. Sorokin, Ratsionalnye approksimatsii i ortogonalnost, Nauka, M., 1988

[2] Dzh. Beiker ml., P. Greivs-Morris, Approksimatsii Pade. 1. Osnovy teorii. 2. Obobscheniya i prilozheniya, Mir, M., 1986, 502 pp.

[3] C. Jacobi, “Über die Darstellung einer Reihe gegebner Werthe durch eine gebrochne rationale Function”, Journal für die reine und angewandte Mathematik, 30 (1846), 127–156 | MR

[4] C. Hermite, “Sur la fonction exponentielle”, Comptes rendus de l'Académie des Sciences, 77 (1873), 18–293

[5] A.P. Starovoitov, N.V. Ryabchenko, “O edinstvennosti reshenii zadach Ermita–Pade”, Vestsi Natsyyanalnai akademii navuk Belarusi. Ser. fizika-matematychnykh navuk, 55:4 (2019), 445–456

[6] A.P. Starovoitov, N.V. Ryabchenko, “O determinantnykh peredstavleniyakh mnogochlenov Ermita–Pade”, Trudy Moskovskogo matematicheskogo obschestva, 83, no. 1, 2022, 17–36