Velikoivanenko, A. I. Multidimensional analogues of the Pólya theorem. (English. Russian original) Zbl 0627.60022 Theory Probab. Math. Stat. 34, 39-46 (1987); translation from Teor. Veroyatn. Mat. Stat. 34, 36-43 (1986). In this article it is shown that a direct generalization of Polya’s theorem on characteristic functions to multidimensional distributions does not hold. A necessary and sufficient condition is proved for a multivariable function to be a characteristic function. In the light of this condition a generalization of Polya’s theorem is discussed. Reviewer: A.M.Mathai MSC: 60E10 Characteristic functions; other transforms 60G60 Random fields Keywords:characteristic functions; multivariable function; Polya’s theorem PDFBibTeX XMLCite \textit{A. I. Velikoivanenko}, Theory Probab. Math. Stat. 34, 39--46 (1987; Zbl 0627.60022); translation from Teor. Veroyatn. Mat. Stat. 34, 36--43 (1986)