Geodesic
An Extremal Problem for the Derivative of a Rational Function
Matematičeskie zametki, Tome 100 (2016) no. 5, pp. 732-738

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

Erdős' well-known problem on the maximum absolute value of the derivative of a polynomial on a connected lemniscate is extended to the case of a rational function. Moreover, under the assumption that certain lemniscates are connected, a sharp upper bound for the absolute value of the derivative of a rational function at any point in the plane different from the poles is found. The role of the extremal function is played by an appropriate Zolotarev fraction.
Keywords: rational function, lemniscate, Riemann surface, symmetrization.
Mots-clés : Zolotarev fraction 
@article{MZM_2016_100_5_a7,
     author = {V. N. Dubinin},
     title = {An {Extremal} {Problem} for the {Derivative} of a {Rational} {Function}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {732--738},
     publisher = {mathdoc},
     volume = {100},
     number = {5},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_100_5_a7/}
}
TY  - JOUR
AU  - V. N. Dubinin
TI  - An Extremal Problem for the Derivative of a Rational Function
JO  - Matematičeskie zametki
PY  - 2016
SP  - 732
EP  - 738
VL  - 100
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2016_100_5_a7/
LA  - ru
ID  - MZM_2016_100_5_a7
ER  - 
%0 Journal Article
%A V. N. Dubinin
%T An Extremal Problem for the Derivative of a Rational Function
%J Matematičeskie zametki
%D 2016
%P 732-738
%V 100
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2016_100_5_a7/
%G ru
%F MZM_2016_100_5_a7
V. N. Dubinin. An Extremal Problem for the Derivative of a Rational Function. Matematičeskie zametki, Tome 100 (2016) no. 5, pp. 732-738. http://geodesic.mathdoc.fr/item/MZM_2016_100_5_a7/