Two-sided estimates of the approximation numbers of certain Volterra integral operators

Edmunds, D.; Evans, W.; Harris, D.

Edmunds, D. ; Evans, W. ; Harris, D.

Studia Mathematica, Tome 122 (1997), p. 59-80 / Harvested from The Polish Digital Mathematics Library

Résumé

We consider the Volterra integral operator $T : L^{p} (ℝ^{+}) \to L^{p} (ℝ^{+})$ defined by $(T f) (x) = v (x) ʃ_{0}^{x} u (t) f (t) d t$ . 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 $l i m_{n \to \infty} n a_{n} (T) = π^{- 1} ʃ_{0}^{\infty} | u (t) v (t) | d t$ . We also provide upper and lower estimates for the $ℓ^{α}$ and weak $ℓ^{α}$ norms of (an(T)) when 1 < α < ∞.

Publié le : 1997-01-01

Zbl 0897.47043

EUDML-ID : urn:eudml:doc:216397

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     author = {D. Edmunds and W. Evans and D. Harris},
     title = {Two-sided estimates of the approximation numbers of certain Volterra integral operators},
     journal = {Studia Mathematica},
     volume = {122},
     year = {1997},
     pages = {59-80},
     zbl = {0897.47043},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv124i1p59bwm}
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Edmunds, D.; Evans, W.; Harris, D. Two-sided estimates of the approximation numbers of certain Volterra integral operators. Studia Mathematica, Tome 122 (1997) pp. 59-80. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv124i1p59bwm/

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