On deviations from rational functions of entire functions of finite lower order

E. Ciechanowicz, and I. I. Marchenko. "On deviations from rational functions of entire functions of finite lower order." Annales Polonici Mathematici 91.2-3 (2007): 161-177. <http://eudml.org/doc/281065>.

@article{E2007,
abstract = {Let f be a transcendental entire function of finite lower order, and let $q_\{ν\}$ be rational functions. For 0 < γ < ∞ let B(γ):= πγ/sinπγ if γ ≤ 0.5, B(γ):= πγ if γ > 0.5. We estimate the upper and lower logarithmic density of the set $\{r: ∑_\{1≤ν≤k\} log⁺ max_\{||z||=r\} |f(z)−q_\{ν\}(z)|^\{−1\} < B(γ)T(r,f)\}$.},
author = {E. Ciechanowicz, I. I. Marchenko},
journal = {Annales Polonici Mathematici},
keywords = {entire function; subharmonic function; logarithmic density},
language = {eng},
number = {2-3},
pages = {161-177},
title = {On deviations from rational functions of entire functions of finite lower order},
url = {http://eudml.org/doc/281065},
volume = {91},
year = {2007},
}

TY - JOUR
AU - E. Ciechanowicz
AU - I. I. Marchenko
TI - On deviations from rational functions of entire functions of finite lower order
JO - Annales Polonici Mathematici
PY - 2007
VL - 91
IS - 2-3
SP - 161
EP - 177
AB - Let f be a transcendental entire function of finite lower order, and let $q_{ν}$ be rational functions. For 0 < γ < ∞ let B(γ):= πγ/sinπγ if γ ≤ 0.5, B(γ):= πγ if γ > 0.5. We estimate the upper and lower logarithmic density of the set ${r: ∑_{1≤ν≤k} log⁺ max_{||z||=r} |f(z)−q_{ν}(z)|^{−1} < B(γ)T(r,f)}$.
LA - eng
KW - entire function; subharmonic function; logarithmic density
UR - http://eudml.org/doc/281065
ER -