Remark to existence theorem for entire functions of bounded $l$-index |
|
| Author | |
| Abstract |
There exists an entire function $f$ with simple zeros
such that for every positive continuous on $[0,+\infty)$ function $l$
satisfying the condition $rl(r)\nearrow+\infty$ as $r\to+\infty$, either
$f$ is of unbounded $l$-index or
$\ln\,M_f(r)=o\left(\int_{0}^r l(t)dt\right)$ as $r\to+\infty$.
|
| Keywords |
entire functions with simple zeros, growth of entire functions, asymptotic growth conditions, integral growth estimates, complex analysis of entire functions
|
| DOI |
doi:10.30970/ms.13.1.97-99
|
Reference |
1. Kuzyk A.D., Sheremeta M.M. Entire functions of bounded value l-distribution. Matematicheskie Zametki, 1986, Vol. 39, No. 1, pp. 3–13. (in Russian)
2. Gol'dberg A.A., Sheremeta M.M. On the existence of an entire transcendental function of bounded l-index. Matematicheskie Zametki, 1995, Vol. 57, No. 1, pp. 125–129. (in Russian) 3. Bordulyak M.T. A proof of Sheremeta's conjecture concerning entire function of bounded l-index. Matematychni Studii, 1999, Vol. 12, No. 1, pp. 108–110. 4. Sheremeta M.M., Kuzyk A.D. On logarithmic derivative and zeros of entire functions of bounded l-index. Sibirskii Matematicheskii Zhurnal, 1992, Vol. 33, No. 2, pp. 142–150. (in Russian) 5. Bratishtshev A.V. On the reversion of l'Hospital rule. Mekhanika sploshnoj sredy, Rostov-on-Don: Izdatelstvo RGU, 1985, pp. 28–42. (in Russian) |
| Pages |
97-99
|
| Volume |
13
|
| Issue |
1
|
| Year |
2000
|
| Journal |
Matematychni Studii
|
| Full text of paper | |
| Table of content of issue |