Geodesic
Exact asymptotic behavior of singular values of a class of integral operators
Czechoslovak Mathematical Journal, Tome 49 (1999) no. 4, pp. 707-732 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We find an exact asymptotic formula for the singular values of the integral operator of the form $\int _{\Omega } T(x,y)k(x-y) \cdot \mathrm{d}y \: L^2 (\Omega )\rightarrow L^2(\Omega )$ ($\Omega \subset \mathbb{R}^m$, a Jordan measurable set) where $k(t) = k_0((t^2_1 + t^2_2 + \ldots t^2_m)^{\frac{m}{2}})$, $k_0 (x) = x^{\alpha -1} L(\tfrac{1}{x})$, $\tfrac{1}{2} - \tfrac{1}{2m} \alpha \tfrac{1}{2}$ and $L$ is slowly varying function with some additional properties. The formula is an explicit expression in terms of $L$ and $T$.
We find an exact asymptotic formula for the singular values of the integral operator of the form $\int _{\Omega } T(x,y)k(x-y) \cdot \mathrm{d}y \: L^2 (\Omega )\rightarrow L^2(\Omega )$ ($\Omega \subset \mathbb{R}^m$, a Jordan measurable set) where $k(t) = k_0((t^2_1 + t^2_2 + \ldots t^2_m)^{\frac{m}{2}})$, $k_0 (x) = x^{\alpha -1} L(\tfrac{1}{x})$, $\tfrac{1}{2} - \tfrac{1}{2m} \alpha \tfrac{1}{2}$ and $L$ is slowly varying function with some additional properties. The formula is an explicit expression in terms of $L$ and $T$.
Classification : 47B10, 47G10 
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     title = {Exact asymptotic behavior of singular values of a class of integral operators},
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}
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Dostanić, Milutin. Exact asymptotic behavior of singular values of a class of integral operators. Czechoslovak Mathematical Journal, Tome 49 (1999) no. 4, pp. 707-732. http://geodesic.mathdoc.fr/item/CMJ_1999_49_4_a4/

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