Exact asymptotic behavior of singular values of a class of integral operators

Author: Dostani cacute M.

Source: Czechoslovak Mathematical Journal, Volume 49, Number 4, December 1999 , pp. 707-732(26)

Publisher: Springer

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Abstract:

We find an exact asymptotic formula for the singular values of the integral operator of the form \int_\Omega T(x,y)k(x-y) \cdot {\rm d}y: L^2 (\Omega) \rightarrow L^2 (\Omega ) \ (\Omega \subset {\Bbb R}^m, a Jordan measurable set) where k(t) = k_0((t^2_1 + t^2_2 + \ldots t^2_m)^{m \over 2}), \ k_0(x) = x^{\alpha-1}L({1 \over x}), \ {1 \over 2} - {1 \over 2m} \lt \alpha \lt {1 \over 2} and L is slowly varying function with some additional properties. The formula is an explicit expression in terms of L and T.

Language: English

Document Type: Research article

Affiliations: 1: Matemati ccaron ki fakultet, Studentski trg 16, 11000 Beograd, Yugoslavia. domi@matf.bg.ac.yuki fakultet, Studentski trg 16, 11000 Beograd, Yugoslavia. domi@matf.bg.ac.yu">