Extremal interpolation in the mean with overlapping averaging intervals and $L$-splines
Izvestiya. Mathematics , Tome 62 (1998) no. 4, pp. 833-856.

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper deals with the problem of extremal interpolation in the mean for large averaging intervals with the minimal value of the norm of a linear differential operator with constant real coefficients in the case when the extremal functions are $L$-splines.
@article{IM2_1998_62_4_a7,
     author = {V. T. Shevaldin},
     title = {Extremal interpolation in the mean with overlapping averaging intervals and $L$-splines},
     journal = {Izvestiya. Mathematics },
     pages = {833--856},
     publisher = {mathdoc},
     volume = {62},
     number = {4},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1998_62_4_a7/}
}
TY  - JOUR
AU  - V. T. Shevaldin
TI  - Extremal interpolation in the mean with overlapping averaging intervals and $L$-splines
JO  - Izvestiya. Mathematics 
PY  - 1998
SP  - 833
EP  - 856
VL  - 62
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1998_62_4_a7/
LA  - en
ID  - IM2_1998_62_4_a7
ER  - 
%0 Journal Article
%A V. T. Shevaldin
%T Extremal interpolation in the mean with overlapping averaging intervals and $L$-splines
%J Izvestiya. Mathematics 
%D 1998
%P 833-856
%V 62
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1998_62_4_a7/
%G en
%F IM2_1998_62_4_a7
V. T. Shevaldin. Extremal interpolation in the mean with overlapping averaging intervals and $L$-splines. Izvestiya. Mathematics , Tome 62 (1998) no. 4, pp. 833-856. http://geodesic.mathdoc.fr/item/IM2_1998_62_4_a7/

[1] Subbotin Yu. N., “Ekstremalnye zadachi funktsionalnoi interpolyatsii i interpolyatsionnye v srednem splainy”, Tr. MIAN SSSR, 138, Nauka, M., 1975, 118–173 | MR | Zbl

[2] Shevaldin V. T., “Nekotorye zadachi ekstremalnoi interpolyatsii v srednem dlya lineinykh differentsialnykh operatorov”, Tr. MIAN SSSR, 164, Nauka, M., 1983, 203–240 | MR | Zbl

[3] Subbotin Yu. N., “O svyazi mezhdu konechnymi raznostyami i sootvetstvuyuschimi proizvodnymi”, Tr. MIAN SSSR, 78, Nauka, M., 1965, 24–42 | MR | Zbl

[4] Subbotin Yu. N., “Ekstremalnaya funktsionalnaya interpolyatsiya v srednem s naimenshim znacheniem $n$-i proizvodnoi pri bolshikh intervalakh usredneniya”, Matem. zametki, 59:1 (1996), 114–132 | MR

[5] Subbotin Yu. N., “Ekstremalnaya v $L_p$ interpolyatsiya v srednem pri peresekayuschikhsya intervalakh usredneniya”, Izv. RAN. Ser. matem., 61:1 (1997), 177–198 | MR | Zbl

[6] Shevaldin V. T., Ekstremalnaya interpolyatsiya dlya lineinykh differentsialnykh operatorov s postoyannymi koeffitsientami, Dis. $\dots $ kand. fiz.-mat. nauk, UrGU, Sverdlovsk, 1983

[7] Krein M. G., “Integralnye uravneniya na polupryamoi s yadrami, zavisyaschimi ot raznosti argumentov”, UMN, 13:5 (1958), 3–120 | MR | Zbl