From Schoenberg to Pick–Nevanlinna: Toward a complete picture of the variogram class

@article{Porcu2011FromST,
  title={From Schoenberg to Pick–Nevanlinna: Toward a complete picture of the variogram class},
  author={Emilio Porcu and Ren{\'e} L. Schilling},
  journal={Bernoulli},
  year={2011},
  volume={17},
  pages={441-455}
}
We show that a large subclass of variograms is closed under products and that some desirable stability properties, such as the product of special compositions, can be obtained within the proposed setting. We introduce new classes of kernels of Schoenberg–Levy type and demonstrate some important properties of rotationally invariant variograms. 

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Addendum to “From Schoenberg to Pick–Nevanlinna: Towards a complete picture of the variogram class”
We are grateful to Prof. Chungsheng Ma who pointed out that our proof of Theorem 8 in [2] uses the continuity of the function γ . For the present proof to work, one has to add ‘continuity’ in the
Priority and correctness on "From Schoenberg to Pick-Nevanlinna: Toward a complete picture of the variogram class" by Porcu and Schilling (2011, arXiv:0812.2936)
It is not the purpose of this correspondence to complain about that six out of seven theorems listed in Porcu and Schilling (arXiv:0812.2936; 2011, Bernoulli) belong to others, but not to the authors
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