Abstract
For regularly convergent functional series, an analog of the classical Borel relation between the maximum of the modulus of a sum and the maximal term of this series is obtained.
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References
V. A. Osokolkov, “On the growth of entire functions represented by regularly convergent functional series, ” Mat. Sb., 100, No. 2, 312–334 (1976).
O. V. Skaskiv, “On the behavior of the maximal term of a Dirichlet series defining an entire function, ” Mat. Zametki, 37, No. 1, 41–47 (1985); English transl. in Math. Notes.
O. B. Skaskiv and O. M. Trusevich, “The maximal term and the sum of a regularly convergent series, ” Lviv Univ. Bull., Ser. Mech.-Math., 49, 75–79 (1998).
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Skaskiv, O.V., Trusevich, O.M. Borel-Type Theorems for Regularly Convergent Functional Series. Journal of Mathematical Sciences 107, 3597–3600 (2001). https://doi.org/10.1023/A:1011946308021
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DOI: https://doi.org/10.1023/A:1011946308021