Geodesic
Free multiple interpolation
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 40, Tome 401 (2012), pp. 103-121 
A. M. Kotochigov. Free multiple interpolation. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 40, Tome 401 (2012), pp. 103-121. http://geodesic.mathdoc.fr/item/ZNSL_2012_401_a5/
@article{ZNSL_2012_401_a5,
     author = {A. M. Kotochigov},
     title = {Free multiple interpolation},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {103--121},
     year = {2012},
     volume = {401},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_401_a5/}
}
TY  - JOUR
AU  - A. M. Kotochigov
TI  - Free multiple interpolation
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2012
SP  - 103
EP  - 121
VL  - 401
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2012_401_a5/
LA  - ru
ID  - ZNSL_2012_401_a5
ER  - 
%0 Journal Article
%A A. M. Kotochigov
%T Free multiple interpolation
%J Zapiski Nauchnykh Seminarov POMI
%D 2012
%P 103-121
%V 401
%U http://geodesic.mathdoc.fr/item/ZNSL_2012_401_a5/
%G ru
%F ZNSL_2012_401_a5

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Our aim in this article is to construct a bounded linear operator that solves the problem of multiple interpolation (interpolation with derivatives). It is proved that such an operator exists for nontangential and sparse interpolation sets if we consider interpolation by analytic functions satisfying the following condition: $|f^{(m)}(z_1)-f^{(m)}(z_2)|\leq\omega(|z_1-z_2|)$.

[1] L. Carleson, “An interpolation problem for bounded analytic functions”, Amer. J. Math., 80:4 (1958), 921–930 | DOI | MR | Zbl

[2] A. M. Kotochigov, “Interpolyatsiya analiticheskimi funktsiyami, gladkimi vplot do granitsy”, Zap. nauchn. semin. LOMI, 30, 1972, 167–169 | MR | Zbl

[3] V. I. Vasyunin, “O chisle serii Karlesona”, Zap. nauchn. seminarov LOMI, 65, 1976, 178–182 | MR | Zbl

[4] A. M. Kotochigov, “Svobodnaya interpolyatsiya v klassakh funktsii s $s$-i proizvodnoi iz klassa Khardi”, Zap. nauchn. semin. POMI, 303, 2003, 169–202 | MR | Zbl

[5] A. M. Kotochigov, “Interpolyatsiya v prostranstvakh analiticheskikh funktsii, opredelyaemykh modulem nepreryvnosti”, Teoriya funktsii, funktsionalnyi analiz i ikh prilozheniya, 41, 1983, 77–90

[6] V. K. Dzyadyk, Vvedenie v teoriyu priblizheniya funktsii polinomami, “Nauka”, Moskva, 1977 | Zbl

[7] P. Kusis, Vvedenie v teoriyu prostranstv $H^p$, “Mir”, Moskva, 1984 | MR

[8] G. M. Goluzin, Geometricheskaya teoriya funktsii kompleksnogo peremennogo, “Nauka”, Moskva, 1966 | MR | Zbl