Exact asymptotic behavior of singular values of a class of integral operators期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Milutin Dostanić

Affiliation:	(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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