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Гайсин, А. М.; Belous, T. I.

doi:10.1023/a:1022004102200

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2022

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Section: Introductionmentioning

confidence: 99%

“…There are many papers on the Hadamard composition of analytic functions and the Dirichlet series [9][10][11]. For example, A. Gaisin and T. Belous [10] studied the maximal term of the Hadamard composition of the Dirichlet series with real exponents. Alower estimate for the sum of a Dirichlet series over a curve arbitrarily approaching the convergence line was obtained.…”

Section: Introductionmentioning

confidence: 99%

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Hadamard Compositions of Gelfond–Leont’ev Derivatives

Sheremeta

2022

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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. The relationship between the growth of the Gelfond–Leont’ev derivative of the Hadamard composition of functions fj and the growth Hadamard composition of Gelfond–Leont’ev derivatives of these functions is studied. We found conditions under which these derivatives and the composition have the same order and a lower order. For the maximal terms of the power expansion of these derivatives, I describe behavior of their ratios.

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