The exact bounds of lower type magnitude for entire function of order $\rho\in(0,1)$ with zeros of prescribed average densities
Ufa mathematical journal, Tome 7 (2015) no. 4, pp. 32-57
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We provide exact two-sided estimates for lower type magnitude of entire functions of order $\rho\in(0,1)$. The zeroes of these functions have prescribed upper and lower average densities and are arbitrarily distributed in the complex plane or on a ray. We analyze the obtained results and compare them them with known facts for entire functions of usual type.
Keywords:
type and lower type of an entire function, the upper and lower average densities of the sequence of zeroes.
@article{UFA_2015_7_4_a3,
author = {G. G. Braichev},
title = {The exact bounds of lower type magnitude for entire function of order $\rho\in(0,1)$ with zeros of prescribed average densities},
journal = {Ufa mathematical journal},
pages = {32--57},
publisher = {mathdoc},
volume = {7},
number = {4},
year = {2015},
language = {en},
url = {http://geodesic.mathdoc.fr/item/UFA_2015_7_4_a3/}
}
TY - JOUR AU - G. G. Braichev TI - The exact bounds of lower type magnitude for entire function of order $\rho\in(0,1)$ with zeros of prescribed average densities JO - Ufa mathematical journal PY - 2015 SP - 32 EP - 57 VL - 7 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/UFA_2015_7_4_a3/ LA - en ID - UFA_2015_7_4_a3 ER -
%0 Journal Article %A G. G. Braichev %T The exact bounds of lower type magnitude for entire function of order $\rho\in(0,1)$ with zeros of prescribed average densities %J Ufa mathematical journal %D 2015 %P 32-57 %V 7 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/UFA_2015_7_4_a3/ %G en %F UFA_2015_7_4_a3
G. G. Braichev. The exact bounds of lower type magnitude for entire function of order $\rho\in(0,1)$ with zeros of prescribed average densities. Ufa mathematical journal, Tome 7 (2015) no. 4, pp. 32-57. http://geodesic.mathdoc.fr/item/UFA_2015_7_4_a3/