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

Milutin R. Dostanić — 1999

Czechoslovak Mathematical Journal

We find an exact asymptotic formula for the singular values of the integral operator of the form Ω T ( x , y ) k ( x - y ) · d y L 2 ( Ω ) L 2 ( Ω ) ( Ω m , a Jordan measurable set) where k ( t ) = k 0 ( ( t 1 2 + t 2 2 + ... t m 2 ) m 2 ) , k 0 ( x ) = x α - 1 L ( 1 x ) , 1 2 - 1 2 m < α < 1 2 and L is slowly varying function with some additional properties. The formula is an explicit expression in terms of L and T .

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