Geodesic
A Bilogarithmic Criterion for the Existence of a Regular Minorant that Does Not Satisfy the Bang Condition
Matematičeskie zametki, Tome 110 (2021) no. 5, pp. 672-687

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Problems of constructing regular majorants for sequences $\mu=\{\mu_n\}_{n=0}^{\infty}$ of numbers $\mu_n\ge0$ 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 $(0,+\infty]$ in terms of the Levinson bilogarithmic condition $M=\{\mu_n^{-1}\}_{n=0}^{\infty}$ 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.
Keywords: entire function, Levinson bilogarithmic condition, regular sequences
Mots-clés : Legendre transform. 
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     author = {R. A. Gaisin},
     title = {A {Bilogarithmic} {Criterion} for the {Existence} of a {Regular} {Minorant} that {Does} {Not} {Satisfy} the {Bang} {Condition}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {672--687},
     publisher = {mathdoc},
     volume = {110},
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     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_110_5_a2/}
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R. A. Gaisin. A Bilogarithmic Criterion for the Existence of a Regular Minorant that Does Not Satisfy the Bang Condition. Matematičeskie zametki, Tome 110 (2021) no. 5, pp. 672-687. http://geodesic.mathdoc.fr/item/MZM_2021_110_5_a2/