Geodesic
On characteristic functions of the multidimensional distributions
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 2, Tome 244 (1997), pp. 143-149

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The problem of extension of the positive definite on bounded domain functions onto the whole space is considered. It is shown that the problem may be reduced to the some problem for functions given on the integer lattice. A criterion providing extension in this case is given also. 
@article{ZNSL_1997_244_a8,
     author = {A. A. Zinger},
     title = {On characteristic functions of the multidimensional distributions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {143--149},
     publisher = {mathdoc},
     volume = {244},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_244_a8/}
}
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A. A. Zinger. On characteristic functions of the multidimensional distributions. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 2, Tome 244 (1997), pp. 143-149. http://geodesic.mathdoc.fr/item/ZNSL_1997_244_a8/