Geodesic
The convergence of interpolating on scalar matrix knots in a class of analytical functions
Trudy Instituta matematiki, Tome 14 (2006) no. 2, pp. 102-111 
L. A. Yanovich; A. V. Tarasevich. The convergence of interpolating on scalar matrix knots in a class of analytical functions. Trudy Instituta matematiki, Tome 14 (2006) no. 2, pp. 102-111. http://geodesic.mathdoc.fr/item/TIMB_2006_14_2_a12/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The minimal regularity domains of functions where the convergence of interpolating on scalar matrix knots on a set of matrices with a given spectrum structure occurs are found. For the case of equidistant scalar matrix knots, the convergence of trigonometrical interpolating in a class of periodic analytical functions is proved.

[1] Krylov V.I., Priblizhennoe vychislenie integralov, M., 1967 | MR

[2] Krylov V.I., “Ob opredelenii naimenshei oblasti, golomorfnost v kotoroi obespechivaet skhodimost ermitovskogo interpolirovaniya pri lyuboi sisteme uzlov”, Dokl. AN SSSR, 78:5 (1951), 857–859 | MR | Zbl

[3] Gantmakher F.R., Teoriya matrits, M., 1967

[4] Kish O., “O skhodimosti trigonometricheskogo interpolirovniya periodicheskikh analiticheskikh funktsii”, Dokl. AN SSSR, 102:3 (1955), 449–450

[5] Krylov V.I., Yanovich L.A., “O skhodimosti trigonometricheskogo interpolirovaniya dlya analiticheskikh periodicheskikh funktsii”, Dokl. AN BSSR, 7:10 (1963), 649–652 | MR | Zbl

[6] Krylov V.I., Yanovich L.A., “O tochnosti priblizheniya periodicheskikh analiticheskikh funktsii interpolyatsionnymi trigonometricheskimi mnogochlenami s ravnootstoyaschimi uzlami”, Dokl. AN BSSR, 9:2 (1965), 73–76 | MR | Zbl

[7] Smirnov V.I., Lebedev N.A., Konstruktivnaya teoriya funktsii kompleksnogo peremennogo, M.; L., 1964 | MR