| Title |
A note about the deterministic property of characteristic functions / |
| Authors |
Norvidas, Saulius |
| DOI |
10.15388/NA.2019.1.9 |
| Full Text |
|
| Is Part of |
Nonlinear analysis: modelling and control.. Vilnius : Vilnius University Institute of Mathematics and Informatics. 2019, vol. 24, iss. 1, p. 150-158.. ISSN 1392-5113. eISSN 2335-8963 |
| Keywords [eng] |
characteristic function ; density function ; entire function ; probability measure ; Bernstein space. |
| Abstract [eng] |
We study an extension property for characteristic functions f : Rn → C of probability measures. More precisely, let f be the characteristic function of a probability density φ on Rn, and let Uσ = {x ∈ Rn: mink|xk| > σ}, σ > 0, be a neighborhood of infinity. We say that f has the σ-deterministic property if for any other characteristic function g such that f = g on Uσ, it follows that f ≡ g. A sufficient condition on f to has the σ-deterministic property is given. We also discuss the question about how precise our sufficient condition is? These results show that the σ-deterministic property of f depends on an arithmetic structure of the support of φ. |
| Published |
Vilnius : Vilnius University Institute of Mathematics and Informatics |
| Type |
Journal article |
| Language |
English |
| Publication date |
2019 |
