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Hadamard Compositions of Gelfond–Leont’ev Derivatives [PDF]

Axioms, 2022
For analytic functions fj(z)=∑n=0∞an,jzn, 1≤j≤p, the notion of a Hadamard composition (f1∗…∗fp)m=∑n=0∞∑k1+⋯+kp=mck1…kpan,1k1·…·an,pkpzn of genus m is introduced.
Myroslav Sheremeta
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On Dirichlet series similar to Hadamard compositions in half-plane

Karpatsʹkì Matematičnì Publìkacìï, 2023
Let $F(s)=\sum\limits_{n=1}^{\infty}a_n\exp\{s\lambda_n\}$ and $F_j(s)=\sum\limits_{n=1}^{\infty}a_{n,j}\exp\{s\lambda_n\},$ $j=\overline{1,p},$ be Dirichlet series with exponents $0\le\lambda_n\uparrow+\infty,$ $n\to\infty,$ and the abscissas of ...
A.I. Bandura, O.M. Mulyava, M.M. Sheremeta   +2 more
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On entire Dirichlet series similar to Hadamard compositions

Математичні Студії, 2023
A function $F(s)=\sum_{n=1}^{\infty}a_n\exp\{s\lambda_n\}$ with $0\le\lambda_n\uparrow+\infty$ is called the Hadamard composition of the genus $m\ge 1$ of functions $F_j(s)=\sum_{n=1}^{\infty}a_{n,j}\exp\{s\lambda_n\}$ if $a_n=P(a_{n,1},...,a_{n,p ...
O.M. Mulyava, M. M. Sheremeta
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The Hadamard compositions of Dirichlet series absolutely converging in half-plane

Математичні Студії, 2020
For Dirichlet series with different finite abscissas of absolute convergence in terms of generalized orders the growth of the Hadamard composition of their derivatives is investigated.
M.M. Sheremeta, O.M. Mulyava
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On Hadamard composition of Gelfond-Leont'ev derivatives of entire and analytic functions in the unit disk

Karpatsʹkì Matematičnì Publìkacìï, 2021
For an entire function and an analytic in the unit disk function the growth of the Hadamard composition of their Gelfond-Leont'ev derivatives is investigated in terms of generalized orders.
O.M. Mulyava, M.M. Sheremeta
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Hadamard compositions of Gelfond-Leont’ev-Sǎlǎgean and Gelfond-Leont’ev-Ruscheweyh derivatives of functions analytic in the unit disk

Математичні Студії, 2020
For analytic functions $$f(z)=z+\sum\limits_{k=2}^{\infty}f_kz^k \mbox{ and } g(z)=z+\sum\limits_{k=2}^{\infty}g_kz^k$$ in the unit disk properties of the Hadamard compositions $D^n_{l,[S]}f*D^n_{l,[S]}g$ and $D^n_{l,[R]}f*D^n_{l,[R]}g$ of their Gelfond ...
M.M. Sheremeta
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On the Relative Φ-Growth of Hadamard Compositions of Dirichlet Series [PDF]

Axioms
For the Dirichlet series F(s)=∑n=1∞fnexp{sλn}, which is the Hadamard composition of the genus m of similar Dirichlet series Fj(s) with the same exponents, the growth with respect to the function G(s) given as the Dirichlet series is studied in terms of ...
Myroslav Sheremeta, Oksana Mulyava
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Relative growth of Hadamard compositions of Dirichlet series absolutely convergent in a half-plane

Математичні Студії
Let $\Lambda=(\lambda_n)$ be a positive sequence increasing to $+\infty$ and $S(\Lambda,A)$ be a class of Dirichlet series $F(s)=\sum\limits_{n=1}^{\infty}a_n\exp \{s\lambda_n\}$ with the abscissa of absolute  convergence $A\in (-\infty,\,+\infty]$.
O.M. Mulyava, M. M. Sheremeta, Yu.S. Trukhan   +2 more
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Relative growth of Hadamard compositions of series in systems of functions [PDF]

Electronic Journal of Mathematics
Myroslav M. Sheremeta
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Belonging to convergence classes of Hadamard compositions of Gelfond-Leont'ev derivatives for analytic functions

Karpatsʹkì Matematičnì Publìkacìï, 2012
The conditions are found, under which the belonging to Valiron convergenceclass of entire functions $f$ and $g$ implies the belonging to thisclass of Gelfond-Leont'ev derivative of Hadamard compositionof functions $f$ and $g$ and of Hadamard composition ...
Mulyava O.M., Sheremeta M.M.
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