Czechoslovak Mathematical Journal, Vol. 49, No. 4, pp. 707-732, 1999

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

Milutin Dostanic

Matematicki fakultet, Studentski trg 16, 11000 Beograd, Yugoslavia, e-mail:

Abstract: We find an exact asymptotic formula for the singular values of the integral operator of the form $\int_{\Omega} T(x,y)k(x-y) \cdot\dd y L^2 (\Omega)\rightarrow L^2(\Omega)$ ($\Omega\subset\Bbb R^m$, a Jordan measurable set) where $k(t) = k_0((t^2_1 + t^2_2 + \ldots t^2_m)^{\frac{m}2})$, $k_0 (x) = x^{\alpha-1} L(\tfrac1x)$, $\tfrac12 - \tfrac1{2m}< \alpha< \tfrac12$ and $L$ is slowly varying function with some additional properties. The formula is an explicit expression in terms of $L$ and $T$.

Classification (MSC 1991): 47B10

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