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

• Autorzy: D. E. Edmunds , W. D. Evans , D. J. Harris
• Języki publikacji: EN

Abstrakty

EN

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 < ∞.

Kategorie tematyczne

• 47G10: Integral operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1997
• Tom: 124
• Numer: 1
• Strony: 59-80

Daty

wydano

1997

otrzymano

1996-03-22

poprawiono

1997-01-13

Twórcy

autor

D. E. Edmunds

• Centre for Mathematical Analysis and its Applications, University of Sussex, Falmer, Brighton BN1 9QH, U.K. ,

autor

W. D. Evans

• School of Mathematics, University of Wales, Cardiff, Senghennydd Road, Cardiff CF2 4YH, U.K. ,

autor

D. J. Harris

• School of Mathematics, University of Wales, Cardiff, Senghennydd Road, Cardiff CF2 4YH, U.K.

Bibliografia

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