A relation between the maximal term and maximum of the modulus of the entire dirichlet series

1992 ◽  
Vol 51 (5) ◽  
pp. 522-526 ◽  
Author(s):  
M. N. Sheremeta
Keyword(s):  
Dirichlet Series ◽  
Entire Dirichlet Series ◽  
Maximal Term

On certain relations between the maximum modulus and the maximal term of an entire dirichlet series

1999 ◽  
Vol 66 (2) ◽  
pp. 223-232 ◽  
Author(s):  
O. B. Skaskiv
Keyword(s):  
Dirichlet Series ◽  
Maximum Modulus ◽  
Entire Dirichlet Series ◽  
Maximal Term

On the Stability of the Maximum Term of the Entire Dirichlet Series

2005 ◽  
Vol 57 (4) ◽  
pp. 686-693
Author(s):  
O. B. Skaskiv ◽  
O. M. Trakalo
Keyword(s):  
Dirichlet Series ◽  
Maximum Term ◽  
Entire Dirichlet Series ◽  
The Stability

On the convergence rate of the partial sums of positive entire Dirichlet series

1991 ◽  
Vol 17 (1) ◽  
pp. 47-54 ◽  
Author(s):  
M. H. Шеремета
Keyword(s):  
Convergence Rate ◽  
Dirichlet Series ◽  
Partial Sums ◽  
Entire Dirichlet Series

A Class of Entire Dirichlet Series as an FK-Space and a Frechet Space

2013 ◽  
Vol 33 (6) ◽  
pp. 1571-1578 ◽  
Author(s):  
Niraj KUMAR ◽  
Garima MANOCHA
Keyword(s):  
Dirichlet Series ◽  
Fréchet Space ◽  
Frechet Space ◽  
Entire Dirichlet Series

Paley Effect for Entire Dirichlet Series

2015 ◽  
Vol 67 (6) ◽  
pp. 838-852
Author(s):  
T. Ya. Hlova ◽  
P. V. Filevych
Keyword(s):  
Dirichlet Series ◽  
Entire Dirichlet Series

scholarly journals Generalized types of the growth of Dirichlet series

2015 ◽  
Vol 7 (2) ◽  
pp. 172-187 ◽  
Author(s):  
T.Ya. Hlova ◽  
P.V. Filevych
Keyword(s):  
Dirichlet Series ◽  
Half Plane ◽  
Maximum Modulus ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Maximal Term ◽  
Necessary And Sufficient ◽  
Nonnegative Sequence

Let $A\in(-\infty,+\infty]$ and $\Phi$ be a continuously on $[\sigma_0,A)$ function such that $\Phi(\sigma)\to+\infty$ as $\sigma\to A-0$. We establish a necessary and sufficient condition on a nonnegative sequence $\lambda=(\lambda_n)$, increasing to $+\infty$, under which the equality$$\overline{\lim\limits_{\sigma\uparrow A}}\frac{\ln M(\sigma,F)}{\Phi(\sigma)}=\overline{\lim\limits_{\sigma\uparrow A}}\frac{\ln\mu(\sigma,F)}{\Phi(\sigma)},$$holds for every Dirichlet series of the form $F(s)=\sum_{n=0}^\infty a_ne^{s\lambda_n}$, $s=\sigma+it$, absolutely convergent in the half-plane ${Re}\, s<A$, where $M(\sigma,F)=\sup\{|F(s)|:{Re}\, s=\sigma\}$ and $\mu(\sigma,F)=\max\{|a_n|e^{\sigma\lambda_n}:n\ge 0\}$ are the maximum modulus and maximal term of this series respectively.

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