Conditions for a radial function in \(R^3\) to be a characteristic function. (English. Ukrainian original) Zbl 0923.60056

Pasenchenko, O. Yu.

Theory Probab. Math. Stat. 55, 161-163 (1997); translation from Teor. Jmovirn. Mat. Stat. 55, 151-153 (1996).

Let \(p(x_1,x_2,x_3)=p(\rho)\), \(\rho=\sqrt{x_1^2+x_2^2+x_3^2}\), be a density of a continuous isotropic distribution in \(R^3\) and let \(f(t_1,t_2,t_3)=f(r), r=\sqrt{t_1^2+t_2^2+t_3^2}.\) Necessary and sufficient conditions under which the function \(f(r)\) is a characteristic function of the distribution \(p(\rho)\) are given.

Reviewer: A.Ya.Olenko (Kyïv)

MSC:

60G60	Random fields
60E10	Characteristic functions; other transforms

Keywords:

random fields; spectral density; correlation; characteristic function