On the boundedness of $l$-$M$- and $l$-$\mu$-index of the Dirichlet series |
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| Author |
Faculty of Mechanics and Mathematics, Lviv Ivan Franko National University
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| Abstract |
We find conditions on the exponents of the Dirichlet series
with an arbitrary abscissa of absolute convergence in order that the
relations
$\ln M(\sigma,F)=O(\Phi(\sigma))$, $\sigma\uparrow A$ and $\ln\mu(\sigma,F)$ = $O(\Phi (\sigma))$,
$\sigma\uparrow A$ be equivalent, where $\Phi$ is a certain convex function
defined on $(-\|,A)$, $A\in(-\|,+\|]$. The obtained result was applied to
proving equivalence of the boundedness of $l$-$M$ and $l$-$\mu$-index
of the Dirichlet series.
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| Keywords |
Dirichlet series, l-M-index, l-mu-index
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| DOI |
doi:10.30970/ms.20.2.143-150
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Reference |
1. Mykytyuk Ja.V., Fedynyak S.I., Sheremeta M.M. Dirichlet series of bounded $l$-$M$-index // Matematychni studii. -- 1999. -- V. 11, № 2. -- P. 159--166.
2. Микитюк Я.В., Сумык О.М., Шеремета М.Н. О функциях, двойственных по Юнгу, и поведении максимальных членов производных ряда Дирихле // Матем. заметки. – 2001. – Т. 69, № 1. – С. 74– 81. 3. Шеремета М.Н., Федыняк С.И. О производной ряда Дирихле // Сиб. матем. журн. – 1998. – Т. 39, № 1. – С. 206–223. 4. Sheremeta M.M., Sumyk O.M. On connection between the growth of maximum modulus and maximal term of entire Dirichlet series in terms of $m$-members asymptotics // Matematychni studii. -- 2003. -- V.~19, № 1. -- P. 83--88. 5. Шеремета М.Н. О поведении максимума модуля целого ряда Дирихле вне исключительного множества // Матем. заметки. – 1995. – Т.57, № 2. – C. 283–296. |
| Pages |
143-150
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| Volume |
20
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| Issue |
2
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| Year |
2003
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| Journal |
Matematychni Studii
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| Full text of paper | |
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