Two-sided estimates of the approximation numbers of certain Volterra integral operators
Studia Mathematica, Tome 124 (1997) no. 1, pp. 59-80
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We consider the Volterra integral operator $T:L^{p}(ℝ^{+}) → L^{p}(ℝ^{+})$ defined by $(Tf)(x) = v(x)ʃ_{0}^{x} u(t)f(t)dt$. Under suitable conditions on u and v, upper and lower estimates for the approximation numbers $a_n(T)$ of T are established when 1 p ∞. When p = 2 these yield $lim_{n→∞} na_{n}(T) = π^{-1} ʃ_{0}^{∞} |u(t)v(t)|dt$. We also provide upper and lower estimates for the $ℓ^{α}$ and weak $ℓ^{α}$ norms of (a_{n}(T)) when 1 α ∞.
@article{10_4064_sm_124_1_59_80,
author = {D. E. Edmunds and },
title = {Two-sided estimates of the approximation numbers of certain {Volterra} integral operators},
journal = {Studia Mathematica},
pages = {59--80},
publisher = {mathdoc},
volume = {124},
number = {1},
year = {1997},
doi = {10.4064/sm-124-1-59-80},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-124-1-59-80/}
}
TY - JOUR AU - D. E. Edmunds AU - TI - Two-sided estimates of the approximation numbers of certain Volterra integral operators JO - Studia Mathematica PY - 1997 SP - 59 EP - 80 VL - 124 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/sm-124-1-59-80/ DO - 10.4064/sm-124-1-59-80 LA - en ID - 10_4064_sm_124_1_59_80 ER -
%0 Journal Article %A D. E. Edmunds %A %T Two-sided estimates of the approximation numbers of certain Volterra integral operators %J Studia Mathematica %D 1997 %P 59-80 %V 124 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/sm-124-1-59-80/ %R 10.4064/sm-124-1-59-80 %G en %F 10_4064_sm_124_1_59_80
D. E. Edmunds; . Two-sided estimates of the approximation numbers of certain Volterra integral operators. Studia Mathematica, Tome 124 (1997) no. 1, pp. 59-80. doi: 10.4064/sm-124-1-59-80
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