Eigenvalues of smooth positive definite kernels
John B. Reade · Proceedings of the Edinburgh Mathematical Society · 1992
For positive definite C1 kernels on a finite real interval the eigenvalues λn are known to be o(1/n2). In this paper this result is shown to be best possible in the best possible sense, namely that, given any decreasing sequence λn, which is o(1/n2), there exist positive definite C1 kernels whose eigenvalues are λn.