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@article{MT_2006_9_1_a3,
author = {E. N. Lomakina and V. D. Stepanov},
title = {Asymptotic {Estimates} for {the~Approximation} and {Entropy} {Numbers} of {a~One-Weight} {Riemann--Liouville} {Operator}},
journal = {Matemati\v{c}eskie trudy},
pages = {52--100},
publisher = {mathdoc},
volume = {9},
number = {1},
year = {2006},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MT_2006_9_1_a3/}
}
TY - JOUR AU - E. N. Lomakina AU - V. D. Stepanov TI - Asymptotic Estimates for the~Approximation and Entropy Numbers of a~One-Weight Riemann--Liouville Operator JO - Matematičeskie trudy PY - 2006 SP - 52 EP - 100 VL - 9 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/MT_2006_9_1_a3/ LA - ru ID - MT_2006_9_1_a3 ER -
%0 Journal Article %A E. N. Lomakina %A V. D. Stepanov %T Asymptotic Estimates for the~Approximation and Entropy Numbers of a~One-Weight Riemann--Liouville Operator %J Matematičeskie trudy %D 2006 %P 52-100 %V 9 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/MT_2006_9_1_a3/ %G ru %F MT_2006_9_1_a3
E. N. Lomakina; V. D. Stepanov. Asymptotic Estimates for the~Approximation and Entropy Numbers of a~One-Weight Riemann--Liouville Operator. Matematičeskie trudy, Tome 9 (2006) no. 1, pp. 52-100. http://geodesic.mathdoc.fr/item/MT_2006_9_1_a3/
[1] Gluskin E. D., “Normy sluchainykh matrits i diametry konechnomernykh mnozhestv”, Mat. sb., 120 (1983), 180–189 | MR | Zbl
[2] Pich A., Operatornye idealy, Mir, M., 1982 | MR
[3] Prokhorov D. V., Stepanov V. D., “Vesovye otsenki operatorov Rimana — Liuvillya i prilozheniya”, Tr. Mat. in-ta im. V. A. Steklova, 243, 2003, 289–312 | MR | Zbl
[4] Carl V., “Entropy numbers of diagonal operators with an application to eigenvalue problems”, J. Approx. Theory, 32:2 (1981), 135–150 | DOI | MR | Zbl
[5] Carl B. and Stephani I., Entropy, Compactness, and the Approximation of Operators, Cambridge Tracts in Mathematics, 98, Cambridge University Press, Cambridge, 1990 | MR | Zbl
[6] Edmunds D. E. and Triebel H., Function Spaces, Entropy Numbers, Differential Operators, Cambridge Tracts in Mathematics, 120, Cambridge University Press, Cambridge, 1996 | MR | Zbl
[7] Edmunds D. E., Evans W. D., and Harris D. J., “Approximation numbers of certain Volterra integral operators”, J. London Math. Soc. (2), 37:2 (1988), 471–489 | DOI | MR | Zbl
[8] Edmunds D. E., Evans W. D., and Harris D. J., “Two-sided estimates of the approximation numbers of certain Volterra inteqral operators”, Studio, Math., 124:1 (1997), 59–80 | MR | Zbl
[9] Lifshits M. A. and Linde W., Approximation and entropy numbers of Volterra operators with application to Brownian motion, Mem. Amer. Math. Soc., 157, no. 745, 2002 | MR
[10] Linde R., “$s$-Numbers of diagonal operators and Besov embeddings”, Rend. Circ. Mat. Palermo (2) Suppl., 1986, no. 10, 83–110 | MR
[11] Lomakina E. and Stepanov V., “On asymptotic behavior of the approximation numbers and estimates of Schatten-von Neumann norms of the Hardy-type integral operators”, Function Spaces and Applications (Delhi, 1997), Narosa Publishing House, New Delhi, 2000, 153–187 | MR | Zbl
[12] Newman J. and Solomyak M., “Two-sided estimates on singular values for a class of integral operators on the semi-axis”, Integral Equations Operator Theory, 20:3 (1994), 335–349 | DOI | MR | Zbl
[13] Prokhorov D. V., “On the boundedness and compactness of a class of integral operators”, J. London Math. Soc. (2), 61:2 (2000), 617–628 | DOI | MR | Zbl
[14] Solomyak M., “Estimates of the approximation numbers of the weighted Riemann–Liouville operator in the spaces $L_p$”, Complex Analysis, Operators, and Related Topics, Oper. Theory Adv. Appl., 113, Birkhäuser, Basel, 2000, 371–383 | MR | Zbl