This question is related to Mercer theorem, Reproducible kernel Hilbert space(RKHS) and interpolation. The wikipedia links are https://en.wikipedia.org/wiki/Mercer%27s_theorem and https://en.wikipedia.org/wiki/Reproducing_kernel_Hilbert_space. As I understand Mercer theorem confirms the existence of RKHS with appropriate kernel. My understanding is that the kernel takes two vector and returns a scalar. Therefore RKHS is nice for classification type application. My question is can we extend the idea to interpolation? In other words if the 'kernel' can take a matrix and a vector it would return a function or a vector. Can we have a similar RKHS space for this case? Is this a valid question? In case it is not, would you please let me know what is the problem in this view?
2026-04-30 01:10:05.1777511405
Can we have extension of Mercer theorem to interpolation?
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