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Definition of Reproducing Kernel

Hi all, I am currently beginning research as a graduate student on meshfree methods, focusing on RKPM right now. I have not been able to find an exact definition of what exactly a reproducing kernel means. Could someone kindly define a reproducing kernel? According to W.K Liu et al, a good example of a reproducing kernel is a Fourier transform, but I can't grasp why is that so.

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