Entire functions with asymptotically multiple-positive sequences of coefficients. (Russian) Zbl 0665.30029
The author’s notion of asymptotically \(m\)-times positive sequence is an extension of the notion of Pólya frequence sequence of order \(m\) (S. Karlin, Total positivity. I (1968; Zbl 0219.47030). The author gives the full description of zero-sets of the class of all entire functions with asymptotically \(m\)-times positive sequences of coefficients and shows that every entire function \(f\) which is positive on the positive half-axis is a quotient of two entire functions from this class.
Reviewer: I.V.Ostrovskij
MSC:
| 30D20 | Entire functions of one complex variable (general theory) |
| 30D10 | Representations of entire functions of one complex variable by series and integrals |
