Geodesic
Estimate of the Norm of the Hermite--Fej\'er Interpolation Operator in Sobolev Spaces
Matematičeskie zametki, Tome 105 (2019) no. 6, pp. 911-925.

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Upper bounds for the norms of Hermite–Fejér interpolation operators in one-dimensional and multidimensional periodic Sobolev spaces are obtained. It is shown that, in the one-dimensional case, the norm of this operator is bounded. In the multidimensional case, the upper bound depends on the ratio of the numbers of nodes on separate coordinates.
Keywords: Hermite–Fejér interpolation operator
Mots-clés : Sobolev spaces. 
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A. I. Fedotov. Estimate of the Norm of the Hermite--Fej\'er Interpolation Operator in Sobolev Spaces. Matematičeskie zametki, Tome 105 (2019) no. 6, pp. 911-925. http://geodesic.mathdoc.fr/item/MZM_2019_105_6_a8/

[1] I. G. Natanson, Konstruktivnaya teoriya funktsii, Nauka, M., 1949 | MR

[2] B. G. Gabdulkhaev, “Approksimatsiya v $H$-prostranstvakh i prilozheniya”, Dokl. AN SSSR, 223:6 (1975), 1293–1296 | MR | Zbl

[3] B. A. Amosov, “O priblizhennom reshenii ellipticheskikh psevdodifferentsialnykh uravnenii na gladkoi zamknutoi krivoi”, Z. Anal. Anwend., 9:6 (1990), 545–563 | DOI | Zbl

[4] B. G. Gabdulkhaev, L. B. Ermolaeva, “Interpolyatsionnye polinomy Lagranzha v prostranstvakh Soboleva”, Izv. vuzov. Matem., 1997, no. 5, 7–19 | MR | Zbl

[5] J. Saranen, G. Vainikko, “Fast solvers of integral and pseudodifferential equations on closed curves”, Math. Comp., 67:224 (1998), 1473–1491 | DOI | MR | Zbl

[6] A. I. Fedotov, “Otsenka normy interpolyatsionnogo operatora Lagranzha v mnogomernom prostranstve Soboleva”, Matem. zametki, 81:3 (2007), 427–433 | DOI | MR | Zbl

[7] A. I. Fedotov, “Convergence of cubature-differences method for multidimensional singular integro-differential equations”, Arch. Math. (Brno), 40:2 (2004), 181–191 | MR | Zbl

[8] A. I. Fedotov, “Otsenka normy interpolyatsionnogo operatora Lagranzha v mnogomernom prostranstve Soboleva s vesom”, Matem. zametki, 99:5 (2016), 752–763 | DOI | MR | Zbl

[9] C. M. Lozinskii, “Ob interpolyatsionnom protsesse Fejer'a”, Dokl. AN SSSR, 24:4 (1939), 318–321 | Zbl

[10] E. M. Zeel, “O trigonometricheskom $(0,p,q)$-interpolirovanii”, Izv. vuzov. Matem., 1970, no. 3, 27–35 | MR | Zbl

[11] E. M. Zeel, “O kratnom trigonometricheskom interpolirovanii”, Izv. vuzov. Matem., 1974, no. 3, 43–51 | MR | Zbl

[12] O. Kish, “O trigonometricheskom $(0,r)$-interpolirovanii”, Acta Math. Acad. Sci. Hungar., 11 (1960), 243–276 | MR

[13] A. Sharma, A. K. Varma, “Trigonometric interpolation”, Duke Math. J., 32:2 (1965), 341–357 | DOI | MR | Zbl

[14] A. K. Varma, “Trigonometric interpolation”, J. Math. Anal. Appl., 28:3 (1969), 652–659 | DOI | MR | Zbl

[15] H. E. Salzer, “New formulas for trigonometric interpolation”, J. Math. and Phys., 39:1 (1960), 83–96 | DOI | MR | Zbl

[16] B. G. Gabdulkhaev, “Kvadraturnye formuly s kratnymi uzlami dlya singulyarnykh integralov”, Dokl. AN SSSR, 227:3 (1976), 531–534 | MR | Zbl

[17] Yu. Soliev, “O kvadraturnykh i kubaturnykh formulakh dlya singulyarnykh integralov s yadrami tipa Koshi”, Izv. vuzov. Matem., 1977, no. 3, 108–112 | MR | Zbl

[18] Yu. Soliev, “Ob interpolyatsionnykh kvadraturnykh formulakh s kratnymi uzlami dlya singulyarnykh integralov”, Izv. vuzov. Matem., 1977, no. 9, 122–126 | MR | Zbl

[19] A. I. Fedotov, “Ob odnom podkhode k postroeniyu kvadraturno-raznostnogo metoda resheniya singulyarnykh integrodifferentsialnykh uravnenii”, Zh. vychisl. matem. i matem. fiz., 29:7 (1989), 978–986 | MR | Zbl

[20] A. I. Fedotov, “Approksimatsiya reshenii singulyarnykh integrodifferentsialnykh uravnenii polinomami Ermita–Feiera”, Ufimsk. matem. zhurn., 10:2 (2018), 109–117

[21] A. Fedotov, “Hermite–Fejér polynomials as an approximate solution of singular integro-differential equations”, Differential and Difference Equations with Applications, Springer Proc. Math. Stat., 230, Springer, Cham, 2017, 93–104 | MR

[22] M. Teilor, Psevdodifferentsialnye operatory, Mir, M., 1985 | MR | Zbl