Geodesic
Zero sets of entire generating functions of Pólya frequency sequences of finite order
Izvestiya. Mathematics, Tome 35 (1990) no. 1, pp. 101-112 
O. M. Katkova; I. V. Ostrovskii. Zero sets of entire generating functions of Pólya frequency sequences of finite order. Izvestiya. Mathematics, Tome 35 (1990) no. 1, pp. 101-112. http://geodesic.mathdoc.fr/item/IM2_1990_35_1_a4/
@article{IM2_1990_35_1_a4,
     author = {O. M. Katkova and I. V. Ostrovskii},
     title = {Zero sets of entire generating functions of {P\'olya} frequency sequences of finite order},
     journal = {Izvestiya. Mathematics},
     pages = {101--112},
     year = {1990},
     volume = {35},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1990_35_1_a4/}
}
TY  - JOUR
AU  - O. M. Katkova
AU  - I. V. Ostrovskii
TI  - Zero sets of entire generating functions of Pólya frequency sequences of finite order
JO  - Izvestiya. Mathematics
PY  - 1990
SP  - 101
EP  - 112
VL  - 35
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/IM2_1990_35_1_a4/
LA  - en
ID  - IM2_1990_35_1_a4
ER  - 
%0 Journal Article
%A O. M. Katkova
%A I. V. Ostrovskii
%T Zero sets of entire generating functions of Pólya frequency sequences of finite order
%J Izvestiya. Mathematics
%D 1990
%P 101-112
%V 35
%N 1
%U http://geodesic.mathdoc.fr/item/IM2_1990_35_1_a4/
%G en
%F IM2_1990_35_1_a4

Voir la notice de l'article provenant de la source Math-Net.Ru

A full description of zero sets of entire generating functions of Pólya frequency sequences of finite order is given. A generalization to the transcendental case of Poincaré's polynomial theorem, relating to the problem of precise determination of the number of positive roots with the help of Descartes' rule, is obtained. Bibliography: 9 titles.

[1] Karlin S., Total positivity, University Press, Stanford, 1968, 576 pp. | MR

[2] Schoenberg I. J., “On the zeros of generating functions of multiply positive sequences and functions”, Annals of Math., 62:3 (1955), 447–471 | DOI | MR | Zbl

[3] Schoenberg I. J., “A note on multiply positive sequences and the Descartes rule of signs”, Rendiconti Circ. Math. Palermo, 4 (1955), 123–131 | DOI | MR | Zbl

[4] Ostrovskii I. V., “O nulevykh mnozhestvakh tselykh periodicheskikh ermitovo-pozitivnykh funktsii”, Teoriya funktsii, funktsion. analiz i ikh prilozh., 37 (1982), 102–110 | MR | Zbl

[5] Poincaré H., “Sur les équations algebriques”, Comptes Rendus, 97 (1383), 1418

[6] Polia G., Sege G., Zadachi i teoremy iz analiza, t. 1, 2, Nauka, M., 1978, 392, 432 s

[7] Fekete M., Polya G., “Ueber ein Problem von Laguerre”, Rendiconti Circ. Math. Palermo, 34 (1912), 89–120 | DOI | Zbl

[8] Kamynin I. P., Ostrovskii I. V., “O nulevykh mnozhestvakh tselykh ermitovo-polozhitelnykh funktsii”, Sib. matem. zhurn., 23:3 (1982), 66–82 | MR | Zbl

[9] Katkova O. M., “Tselye funktsii s asimptoticheski kratno polozhitelnymi posledovatelnostyami koeffitsientov”, Teoriya funktsii, funktsion. analiz i ikh prilozh., 49 (1988), 51–59 | MR | Zbl