Geodesic
A Lower Bound for the Number of Negative Zeros of Power Series
Canadian mathematical bulletin, Tome 22 (1979) no. 1, pp. 47-52

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we are concerned with power series of the type 1 which admit unique analytic extension onto a domain containing the negative real axis. Our primary object is to establish a general theorem giving a lower estimate for the number of different zeros of (1) on the negative real axis. W. Jurkat and A. Peyerimhoff showed that for a certain class of coefficient functions a(z) the number of negative zeros of (1) is closely related to the behaviour of a(z) at z = 0. In particular they proved the following theorem [4, p. 219, Theorem 4]. 
Gawronski, W. A Lower Bound for the Number of Negative Zeros of Power Series. Canadian mathematical bulletin, Tome 22 (1979) no. 1, pp. 47-52. doi: 10.4153/CMB-1979-007-5
@article{10_4153_CMB_1979_007_5,
     author = {Gawronski, W.},
     title = {A {Lower} {Bound} for the {Number} of {Negative} {Zeros} of {Power} {Series}},
     journal = {Canadian mathematical bulletin},
     pages = {47--52},
     year = {1979},
     volume = {22},
     number = {1},
     doi = {10.4153/CMB-1979-007-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1979-007-5/}
}
TY  - JOUR
AU  - Gawronski, W.
TI  - A Lower Bound for the Number of Negative Zeros of Power Series
JO  - Canadian mathematical bulletin
PY  - 1979
SP  - 47
EP  - 52
VL  - 22
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1979-007-5/
DO  - 10.4153/CMB-1979-007-5
ID  - 10_4153_CMB_1979_007_5
ER  - 
%0 Journal Article
%A Gawronski, W.
%T A Lower Bound for the Number of Negative Zeros of Power Series
%J Canadian mathematical bulletin
%D 1979
%P 47-52
%V 22
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1979-007-5/
%R 10.4153/CMB-1979-007-5
%F 10_4153_CMB_1979_007_5

[1] 1. Butzer, P. L. and Nessel, R. J., Fourier Analysis and Approximation, vol. I, Academic Press, New York, London, 1971. Google Scholar

[2] 2. Gawronski, W. and Peyerimhoff, A., On the zeros of power series with rational coefficients, Arch. Math., XXIX (1977), Fasc. 2, 173-186. Google Scholar

[3] 3. Hille, E., Analytic Function Theory, vol. II, Blaisdell Pub. Comp., Waltham Mass., Toronto, London, 1962. Google Scholar

[4] 4. Jurkat, W. B. and Peyerimhoff, A., On power series with negative zeros, Tôhoku Math. J., vol. 24, no. 2, 207-221. Google Scholar

[5] 5. Lindelöf, E., Le calcul des résidus, Chelsea Pub. Comp., New York, 1947. Google Scholar

[6] 6. Peyerimhoff, A., On the zeros of power series, Mich. Math. J., vol. 13 (1966), 193-214. Google Scholar

[7] 7. Polya, G., On the zeros of an integral function represented by Fourier's Integral, Messenger of Math., 3 (1923), 185-188. Google Scholar

[8] 8. Polya, G. und Szegö, G., Aufgaben und Lehrsàtze aus der Analysis I, Springer Verlag, Berlin, Heidelberg, New York, 1970. Google Scholar

Cité par Sources :