Eigenvalues of integral operators with smooth positive definite kernels (Q1097455)

The author studies the asymptotic eigenvalue behaviour of integral operators with positive definite kernels compact d-dimensional infinite differentiable manifolds. The main result is: Let M be a compact d- dimensional \(C^{\infty}\)-manifold equipped with a finite Lebesgue-type measure \(\mu\) and let \(0<t<\infty\). Then for every positive kernel \(K\in C^{t,0}(M,M)\), \(\lambda_ n(T_{K,\mu})=0(n^{-t/d-1}).\) Here \(T_{k,\mu}\) is the integral operator with the kernel K and \(\lambda_ n(T_{K,\mu})\) is the eigenvalue of order n.