积分算子的奇异数和本征值Ⅱ

最近 Rcade 改进了关于 Wcyl 对称核 K(x,y)∈C~1 的本征值为 λ_n(K)=o(n~(-3/2))的经典估计.他把C~1假定放宽为假设 K(x,y)∈L~2(Ω),K(x,y) 按每个变数分别地绝对连续,而且和都在L~2(Ω)中,这里Ω=(0,1)×(0,1),他证明了sum from (n~2λn~2(k)<∞).在前一篇文章3]中,在 Rcade 的条件下得到.本文把这个结论推广到更一般的情况.

Singular Numbers and Eigenvalues of Integral OperatorsⅡ

Rcadc has recently improved Wcyl's classical estimate for the eigenvalues of a symmetric kernel K(x,y) C1 by relaxing the C1 hypothesis to the assumptions that K(x,y) L2, that K(x,y) is absolutely continuous in each variableseparately, and that and are both in , where=0,1]x0,1]. He hasshown that In a previous paper 3] it is obtained that under the reade'sconditions In this paper we extend this resultto the more general cases.