Geodesic
To the interpolation theory of differential operators of arbitrary order in partial derivatives
Trudy Instituta matematiki, Tome 25 (2017) no. 2, pp. 11-20 
M. V. Ignatenko. To the interpolation theory of differential operators of arbitrary order in partial derivatives. Trudy Instituta matematiki, Tome 25 (2017) no. 2, pp. 11-20. http://geodesic.mathdoc.fr/item/TIMB_2017_25_2_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

This article is devoted to the problem of construction and research of the Lagrange interpolation formulas and formulas of the Hermite type with nodes of the second multiplicity for differential operators of arbitrary order in partial derivatives given in the space of continuously differentiable functions of many variables. The construction of operator interpolation formulas is based on interpolation polynomials for scalar functions with respect to the arbitrary Chebyshev system of functions. An explicit representation of the interpolation error has been obtained.

[1] Yanovich L. A., Ignatenko M. V., “Formuly operatornogo interpolirovaniya, osnovannye na interpolyatsionnykh mnogochlenakh dlya chislovykh funktsii”, Trudy Instituta Matematiki NAN Belarusi, 11, Sb. nauch. tr. K 100-letiyu so dnya rozhdeniya akademika V. I. Krylova (2002), 157–167

[2] Ignatenko M. V., Yanovich L. A., “Ob odnom klasse formul operatornogo interpolirovaniya v prostranstve differentsiruemykh funktsii”, Vestsi NAN Belarusi. Ser. fiz.-mat. navuk, 2004, no. 1, 5–11 | MR

[3] Yanovich L. A., Ignatenko M. V., “Ob odnom klasse interpolyatsionnykh mnogochlenov dlya nelineinykh obyknovennykh differentsialnykh operatorov”, Matematicheskoe modelirovanie, 26:11 (2014), 90–96 | MR | Zbl

[4] Ignatenko M. V., Yanovich L. A., “K teorii interpolirovaniya Ermita–Birkgofa nelineinykh obyknovennykh differentsialnykh operatorov”, Vestsi NAN Belarusi. Ser. fiz.-mat. navuk, 2017, no. 2, 7–23

[5] Makarov V. L., Khlobystov V. V., Yanovich L. A., “Methods of Operator Interpolation”, Proc. of the Institute of Mathematics of NAS of Ukraine, 83, Kiev, 2010, 1–517 | MR

[6] Yanovich L. A., Ignatenko M. V., Osnovy teorii interpolirovaniya funktsii matrichnykh peremennykh, Belarus. navuka, Minsk, 2016