科研之友
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摘要
We consider compact Hankel operators realized in l(2)(Z(+)) as infinite matrices Gamma with matrix elements h(j + k). Roughly speaking, we show that if h(j) similar to (b(1) + (-1)(j)b-1) j(-1) (log j)(-alpha) as j -> infinity. for some or alpha > 0, then the eigenvalues of Gamma satisfy lambda(+/-)(n)(Gamma)similar to c(+/-)n(-alpha) as n -> infinity. The asymptotic coefficients c(+) are explicitly expressed in terms of the asymptotic coefficients b1 and b1. Similar results are obtained for Hankel operators Gamma realized in L-2(R+) as integral operators with kernels h(t + s). In this case, the asymptotics of eigenvalues lambda(perpendicular to)(n) (Gamma)are determined by the behavior of h(t) as t -> 0 and as t -> infinity.
- 出版日期2015
