Geodesic
Positive definite functions as an instrument of mathematical analysis
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 7, pp. 67-95

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For the subject in question, the paper describes its connections that are close to the author's interests with branches of functional analysis. The present survey may be suitable as a basis for a special course. 
@article{FPM_2012_17_7_a4,
     author = {E. A. Gorin},
     title = {Positive definite functions as an instrument of mathematical analysis},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {67--95},
     publisher = {mathdoc},
     volume = {17},
     number = {7},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2012_17_7_a4/}
}
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E. A. Gorin. Positive definite functions as an instrument of mathematical analysis. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 7, pp. 67-95. http://geodesic.mathdoc.fr/item/FPM_2012_17_7_a4/