Estimates for the widths of discrete function classes generated by a~two-weight summation operator
Informatics and Automation, Modern problems of mathematics, mechanics, and mathematical physics. II, Tome 294 (2016), pp. 308-324.

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

Order estimates are obtained for the Kolmogorov, linear, and Gel'fand widths of the image of the unit ball of the space $l_p$ under the action of a two-weight summation operator with weights of special kind. Some limit conditions on the parameters defining the weights are considered.
@article{TRSPY_2016_294_a19,
     author = {A. A. Vasil'eva},
     title = {Estimates for the widths of discrete function classes generated by a~two-weight summation operator},
     journal = {Informatics and Automation},
     pages = {308--324},
     publisher = {mathdoc},
     volume = {294},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2016_294_a19/}
}
TY  - JOUR
AU  - A. A. Vasil'eva
TI  - Estimates for the widths of discrete function classes generated by a~two-weight summation operator
JO  - Informatics and Automation
PY  - 2016
SP  - 308
EP  - 324
VL  - 294
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2016_294_a19/
LA  - ru
ID  - TRSPY_2016_294_a19
ER  - 
%0 Journal Article
%A A. A. Vasil'eva
%T Estimates for the widths of discrete function classes generated by a~two-weight summation operator
%J Informatics and Automation
%D 2016
%P 308-324
%V 294
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2016_294_a19/
%G ru
%F TRSPY_2016_294_a19
A. A. Vasil'eva. Estimates for the widths of discrete function classes generated by a~two-weight summation operator. Informatics and Automation, Modern problems of mathematics, mechanics, and mathematical physics. II, Tome 294 (2016), pp. 308-324. http://geodesic.mathdoc.fr/item/TRSPY_2016_294_a19/

[1] Bennett G., “Some elementary inequalities. III”, Q. J. Math. Oxford. Ser. 2, 42:166 (1991), 149–174 | DOI | MR | Zbl

[2] Edmunds D. E., Lang J., “Approximation numbers and Kolmogorov widths of Hardy-type operators in a non-homogeneous case”, Math. Nachr., 297:7 (2006), 727–742 | DOI | MR

[3] Evans W. D., Harris D. J., Lang J., “The approximation numbers of Hardy-type operators on trees”, Proc. London Math. Soc. Ser. 3, 83:2 (2001), 390–418 | DOI | MR | Zbl

[4] Garnaev A. Yu., Gluskin E. D., “O poperechnikakh evklidova shara”, DAN SSSR, 277:5 (1984), 1048–1052 | MR | Zbl

[5] Gluskin E. D., “Normy sluchainykh matrits i poperechniki konechnomernykh mnozhestv”, Mat. sb., 120(162):2 (1983), 180–189 | MR | Zbl

[6] Haroske D. D., Skrzypczak L., “Entropy and approximation numbers of embeddings of function spaces with Muckenhoupt weights. I”, Rev. Mat. Complut., 21:1 (2008), 135–177 | DOI | MR | Zbl

[7] Haroske D. D., Skrzypczak L., “Entropy and approximation numbers of embeddings of function spaces with Muckenhoupt weights. II: General weights”, Ann. Acad. Sci. Fenn. Math., 36:1 (2011), 111–138 | DOI | MR | Zbl

[8] Kashin B. S., “O kolmogorovskikh poperechnikakh oktaedrov”, DAN SSSR, 214:5 (1974), 1024–1026

[9] Kashin B. S., “O poperechnikakh oktaedrov”, UMN, 30:4 (1975), 251–252 | MR | Zbl

[10] Kashin B. S., “Poperechniki nekotorykh konechnomernykh mnozhestv i klassov gladkikh funktsii”, Izv. AN SSSR. Ser. mat., 41:2 (1977), 334–351 | MR | Zbl

[11] Lifshits M. A., “Bounds for entropy numbers for some critical operators”, Trans. Amer. Math. Soc., 364:4 (2012), 1797–1813 | DOI | MR | Zbl

[12] Lifshits M. A., Linde W., Approximation and entropy numbers of Volterra operators with application to Brownian motion, Mem. AMS, 157, Amer. Math. Soc., Providence, RI, 2002 | MR

[13] Lifshits M., Linde W., “Compactness properties of weighted summation operators on trees”, Stud. math., 202:1 (2011), 17–47 | DOI | MR | Zbl

[14] Lifshits M., Linde W., “Compactness properties of weighted summation operators on trees – the critical case”, Stud. math., 206:1 (2011), 75–96 | DOI | MR | Zbl

[15] Lomakina E. N., Stepanov V. D., “On asymptotic behaviour of the approximation numbers and estimates of Schatten–von Neumann norms of the Hardy-type integral operators”, Function spaces and applications, Proc. Int. Conf. (New Delhi, 1997), Narosa Publ. House, New Delhi, 2000, 153–187 | MR | Zbl

[16] Lomakina E. N., Stepanov V. D., “Asimptoticheskie otsenki approksimativnykh i entropiinykh chisel odnovesovogo operatora Rimana–Liuvillya”, Mat. trudy, 9:1 (2006), 52–100 | MR | Zbl

[17] Pietsch A., “$s$-Numbers of operators in Banach spaces”, Stud. math., 51 (1974), 201–223 | MR | Zbl

[18] Stepanets A. I., Methods of approximation theory, Koninklijke Brill NV, Leiden, 2005 | MR

[19] Stesin M. I., “Aleksandrovskie poperechniki konechnomernykh mnozhestv i klassov gladkikh funktsii”, DAN SSSR, 220:6 (1975), 1278–1281 | MR | Zbl

[20] Tikhomirov V. M., “Poperechniki mnozhestv v funktsionalnykh prostranstvakh i teoriya nailuchshikh priblizhenii”, UMN, 15:3 (1960), 81–120 | MR | Zbl

[21] Vasil'eva A. A., “Widths of weighted Sobolev classes on a John domain: Strong singularity at a point”, Rev. Mat. Complut., 27:1 (2014), 167–212 | DOI | MR | Zbl

[22] Vasil'eva A. A., “Widths of function classes on sets with tree-like structure”, J. Approx. Theory, 192 (2015), 19–59 | DOI | MR | Zbl

[23] Vasileva A. A., “Poperechniki vesovykh klassov Soboleva na oblasti s pikom”, Mat. sb., 206:10 (2015), 37–70 | DOI | MR | Zbl

[24] Vasil'eva A. A., “Estimates for $n$-widths of two-weighted summation operators on trees”, Math. Notes, 99:2 (2016), 243–252 | DOI | MR | Zbl