The Bohr radius and the Hadamard convolution operator. (English) Zbl 1543.30006
J. Math. Anal. Appl. 531, No. 1, Part 2, Article ID 127782, 14 p. (2024); corrigendum ibid. 538, No. 2, Article ID 128491, 2 p. (2024).
Summary: The concept of the Bohr radius of a pair of operators is introduced. In terms of the convolution function, a general formula for calculating the Bohr radius of the Hadamard convolution type operator with a fixed initial coefficient is obtained. We apply this formula to the problems of the Bohr radius of the operators of differentiation and integration. Using the concept of the Bohr radius of a pair of operators, we generalize the theorem of B. Bhowmik and N. Das [J. Math. Anal. Appl. 462, No. 2, 1087–1098 (2018; Zbl 1391.30003)] on the comparison of majorant series of subordinate functions.
MSC:
| 30B10 | Power series (including lacunary series) in one complex variable |
| 30A10 | Inequalities in the complex plane |
Citations:
Zbl 1391.30003References:
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