Is there one to one relation Positive definite(PD) matrix and PD function?

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Is it correct to say that a PD matrix can be built from a PD function? For example circulant matrix or Toeplitz seems to be built from a positive definite function. Positive definite function is defined in: https://en.wikipedia.org/wiki/Positive-definite_function . My question is does every positive definite matrix have a corresponding positive definite function? For example there are positive definite matrix which is neither circulant nor Toeplitz, can we have some positive definite function to build such matrix?