Singular numbers of a weighted convolution operator

This article studies a convolution operator on $[0,2\pi]$ with $2\pi$-periodic kernel. The operator acts from $L_2(0,2\pi)$ to $L_2(0,2\pi;\mu)$ where $\mu$ is a Borel measure. An asymptotic formula is obtained for the singular numbers in the case of kernels satisfying a certain regularity condition and of measures with continuous densities. Examples and counterexamples are given.
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