Geodesic
Applications of the Schwarz lemma to inequalities for entire functions with constraints on zeros
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 21, Tome 337 (2006), pp. 101-112

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

It is shown that new inequalities for certain classes of entire functions can be obtained by applying the Schwarz lemma and its generalizations to specially constructed Blaschke products. In particular, for entire functions of exponential type whose zeros lie in the closed lower half-plane, distortion theorems, including the two-point distortion theorem on the real axis, are proved. Similar results are established for polynomials with zeros in the closed unit disk. The classical theorems by Turan and Ankeny–Rivlin are refined. In addition, a theorem on the mutual disposition of the zeros and critical points of a polynomial is proved. Bibliography: 16 titles. 
@article{ZNSL_2006_337_a6,
     author = {V. N. Dubinin},
     title = {Applications of the {Schwarz} lemma to inequalities for entire functions with constraints on zeros},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {101--112},
     publisher = {mathdoc},
     volume = {337},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_337_a6/}
}
TY  - JOUR
AU  - V. N. Dubinin
TI  - Applications of the Schwarz lemma to inequalities for entire functions with constraints on zeros
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2006
SP  - 101
EP  - 112
VL  - 337
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2006_337_a6/
LA  - ru
ID  - ZNSL_2006_337_a6
ER  - 
%0 Journal Article
%A V. N. Dubinin
%T Applications of the Schwarz lemma to inequalities for entire functions with constraints on zeros
%J Zapiski Nauchnykh Seminarov POMI
%D 2006
%P 101-112
%V 337
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2006_337_a6/
%G ru
%F ZNSL_2006_337_a6
V. N. Dubinin. Applications of the Schwarz lemma to inequalities for entire functions with constraints on zeros. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 21, Tome 337 (2006), pp. 101-112. http://geodesic.mathdoc.fr/item/ZNSL_2006_337_a6/