Geodesic
Conditionally positively definite functions on locally compact groups and the Levy--Khinchin formula
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part V, Tome 123 (1983), pp. 46-57

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The Levy–Khinchin formula for conditionally positively definite functions on compactly generated groups is proved. The proof is based on the Choquet's theory. Some examples and applications to 1-cohomology of unitary representations of locally compact groups are considered. 
@article{ZNSL_1983_123_a2,
     author = {S. I. Karpushev},
     title = {Conditionally positively definite functions on locally compact groups and the {Levy--Khinchin} formula},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {46--57},
     publisher = {mathdoc},
     volume = {123},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1983_123_a2/}
}
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S. I. Karpushev. Conditionally positively definite functions on locally compact groups and the Levy--Khinchin formula. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part V, Tome 123 (1983), pp. 46-57. http://geodesic.mathdoc.fr/item/ZNSL_1983_123_a2/