A proof of a Sheremeta conjecture concerning entire function of bounded $l$-index |
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| Author |
Department of Mechanics and Mathematics, Lviv University,Univetrsytetska 1, 290602, Lviv, Ukraine
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| Abstract |
We proved the Sheremeta conjecture on existence for entire function
$f$ of bounded multiplicities of zeros a
positive continuous on $[0;+\infty)$ function $ l$ such
that $f$ is of bounded $l$-index.
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| Keywords |
entire function, bounded multiplicities of zeros, positive continuous function, Sheremeta conjecture
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| DOI |
doi:10.30970/ms.12.1.108-110
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Reference |
1. Kuzyk A.D., Sheremeta M.N. Entire functions of bounded $l$-distribution of values // Matem. zametki. -- 1986 V. 39 № 1 p. 3--13 (in Russian)
2. Gol'dberg A.A., Sheremeta M.N. On existence of entire transcendental function of bounded $l$-index // Matem. zametki. -- 1995 V. 57 № 1 p. 125--129 (in Russian) 3. Bordulyak M.T., Sheremeta M.M. On existence of entire functions of bounded $l$-index and $l$-regular growth // Ukr. matem. zh. -- 1996 V. 48 № 9 p. 1166--1182 (in Russian) 4. Sheremeta M.M. Five open problems in the theory of entire functions // Matem. studii. – 1996 V. 6 № p. 157–159 (in Ukrainian) |
| Pages |
108-110
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| Volume |
12
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| Issue |
1
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| Year |
1999
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| Journal |
Matematychni Studii
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