On the New Description of Exceptional Sets in Asymptotic Estimates for the Entire Functions and the Laplace–Stieltjes Integrals
We obtain a new extended description of the exceptional set in the asymptotic Borel-type relation in terms of the maximum of the integrand function for the Laplace–Stieltjes integrals. The obtained description of an exceptional set in the Borel-type relation leaves no room for improvement. In partic...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-02-01
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| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/14/2/134 |
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| Summary: | We obtain a new extended description of the exceptional set in the asymptotic Borel-type relation in terms of the maximum of the integrand function for the Laplace–Stieltjes integrals. The obtained description of an exceptional set in the Borel-type relation leaves no room for improvement. In particular, we construct a corresponding measure, a function given by the Laplace–Stieltjes integral with respect to this measure, and a measurable set for which the opposite inequality to the Borel-type relation is fulfilled. |
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| ISSN: | 2075-1680 |