On the growth  of Laplace-Stieltjes integrals

Sheremeta, М. М.; Kuryliak, A. O.

doi:10.15330/ms.50.1.22-35

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2023

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Cited by 3 publications

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“…and �.�; I / WD max fjf .x/je x� W x � 0g ; � 2 R; is the maximum of the integrand. It is clear that if f .x/ � 0 for all x � 0; then M.�; I / D I.� / and the asymptotic properties of integrals of this kind were studied in [1]. If � M is the abscissa of convergence of the integral (3) and � � is the abscissa of maximum of the integrand, then…”

Section: Introductionmentioning

confidence: 99%

On Banach Spaces and Fréchet Spaces of Laplace–Stieltjes Integrals

Kuryliak

Sheremeta

2023

J Math Sci

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Section: Introductionmentioning

confidence: 99%

On Banach Spaces and Fréchet Spaces of Laplace–Stieltjes Integrals

Kuryliak

Sheremeta

2023

J Math Sci

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Design of a Two-Layer Al–Al2O3 Coating with an Oxide Layer Formed by the Plasma Electrolytic Oxidation of Al for the Corrosion and Wear Protections of Steel

2023

Prog. Phys. Met.

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Elementary Remarks to the Relative Growth of Series by the System of Mittag-Leffler Functions

Mulyava

2022

BMJ

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For a regularly converging in ${\Bbb C}$ series $F_{\varrho}(z)=\sum\limits_{n=1}^{\infty} a_n E_{\varrho}(\lambda_nz)$, where $0<\varrho<+\infty$ and $E_{\varrho}(z)=\sum\limits_{k=0}^{\infty}\frac{z^k}{\Gamma(1+k/\varrho)}$ is the Mittag-Leffler function, it is investigated the asymptotic behavior of the function $E_{\varrho}^{-1} (M_{F_{\varrho}}(r))$, where $M_f(r)=\max\{|f(z)|:\,|z|=r\}$. For example, it is proved that if $\varlimsup\limits_{n\to \infty}\frac{\ln\,\ln\,n}{\ln\,\lambda_n}\le \varrho$ and $a_n\ge 0$ for all $n\ge 1$, then $\varlimsup\limits_{r\to+\infty}\frac{\ln\,E^{-1}_{\varrho}(M_{F_{\varrho}}(r))}{\ln\,r}=\frac{1}{1-\overline{\gamma}\varrho}$, where $\overline{\gamma}=\varlimsup\limits_{n\to\infty}\frac{\ln\,\lambda_n}{\ln\,\ln\,(1/a_n)}$. A similar result is obtained for the Laplace-Stiltjes type integral $I_{\varrho}(r) = \int\limits_{0}^{\infty}a(x)E_{\varrho}(r x) d F(x)$.

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On the growth of Laplace-Stieltjes integrals

Cited by 3 publications

References 4 publications

On Banach Spaces and Fréchet Spaces of Laplace–Stieltjes Integrals

On Banach Spaces and Fréchet Spaces of Laplace–Stieltjes Integrals

Design of a Two-Layer Al–Al2O3 Coating with an Oxide Layer Formed by the Plasma Electrolytic Oxidation of Al for the Corrosion and Wear Protections of Steel

Elementary Remarks to the Relative Growth of Series by the System of Mittag-Leffler Functions

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