A Bilogarithmic Criterion for the Existence of a Regular Minorant that Does Not Satisfy the Bang Condition

Problems of constructing regular majorants for sequences of numbers that are the Taylor coefficients of integer transcendental functions of minimal exponential type are investigated. A new criterion for the existence of regular minorants of associated sequences of the extended half-line in terms of...

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Bibliographic Details
Published in:Mathematical Notes 2021-11, Vol.110 (5-6), p.666-678
Main Author: Gaisin, R. A.
Format: Article
Language:English
Subjects:
14/34
639/766/189
639/766/530
639/766/747
Criteria
Mathematics
Mathematics and Statistics
Transcendental functions
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Summary:Problems of constructing regular majorants for sequences of numbers that are the Taylor coefficients of integer transcendental functions of minimal exponential type are investigated. A new criterion for the existence of regular minorants of associated sequences of the extended half-line in terms of the Levinson bilogarithmic condition is obtained. The result provides a necessary and sufficient condition for the nontriviality of the important subclass defined by J. A. Siddiqi. The proofs of the main statements are based on properties of the Legendre transform.
ISSN:0001-4346
1067-9073
1573-8876
DOI:10.1134/S0001434621110031