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

Authors:	Milutin Dostani?

Institution:	(1) Matematiki fakultet, Studentski trg 16, 11000 Beograd, Yugoslavia

Abstract:	We find an exact asymptotic formula for the singular values of the integral operator of the form $\int {_\Omega } T(x,y)k(x - y) \cdot {\text{d}}y:L^2 (\Omega ) \to L^2 (\Omega )(\Omega \subset \mathbb{R}^m$ , a Jordan measurable set) where $k(t) = k_0 ((t_1^2 + t_2^2 + ...t_m^2 )^{\tfrac{m}{2}} ),k_0 (x) = x^{\alpha - 1} L(\tfrac{1}{x}),\tfrac{1}{2} - \tfrac{1}{{2m}} < \alpha < \tfrac{1}{2}$ and L is slowly varying function with some additional properties. The formula is an explicit expression in terms of L and T.

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