Eigenvalues of Positive Definite Kernels II

Abstract

We prove what we conjectured in our earlier paper of the same title [SIAM J. Math. Anal., 14 (1983), pp. 152–157], that the eigenvalues of any p times continuously differentiable positive definite kernel are $o({1 / {n^{p + 1} }})$. The method is the same as we used to prove the case $p = 1$ except that we now approximate the kernel by trigonometric polynomials obtained from certain combinations of Jackson kernels.