| Title |
On an uniqueness theorem for characteristic functions / |
| Authors |
Norvidas, Saulius |
| DOI |
10.15388/NA.2017.3.9 |
| Full Text |
|
| Is Part of |
Nonlinear analysis : modelling and control.. Vilnius : Vilnius University Institute of Mathematics and Informatics. 2017, Vol. 22, No. 3, p. 412-420.. ISSN 1392-5113 |
| Keywords [eng] |
Bochner’s theorem ; characteristic function ; Fourier algebra ; positive definite function ; imaginary part of the characteristic function |
| Abstract [eng] |
Suppose that f is the characteristic function of a probability measure on the real line R. We deal with the following open problem posed by N.G. Ushakov: Is it true that f is never determined by its imaginary part =f? In other words, is it true that for any characteristic function f, there exists a characteristic function g such that =f = =g, but f 6= g? The answer to this question is no. We give a characterization of those characteristic functions, which are uniquely determined by their imaginary parts. Also, several examples of characteristic functions, which are uniquely determined by their imaginary parts, are given. |
| Published |
Vilnius : Vilnius University Institute of Mathematics and Informatics |
| Type |
Journal article |
| Language |
English |
| Publication date |
2017 |
| CC license |
|
