A Version of the Malliavin–Rubel Theorem on Entire Functions of Exponential Type with Zeros near the Imaginary Axis

— Let and be two distributions of points on the complex plane . In the case of and , lying on the positive half-line , the classic Malliavin–Rubel theorem from the 1960s, gives a necessary and sufficient correlation between and , when for each entire function exponential type that vanishes on , ther...

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Bibliographic Details
Published in:Russian mathematics 2022-08, Vol.66 (8), p.37-45
Main Author: Salimova, A. E.
Format: Article
Language:English
Subjects:
Entire functions
Mathematics
Mathematics and Statistics
Theorems
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Summary:— Let and be two distributions of points on the complex plane . In the case of and , lying on the positive half-line , the classic Malliavin–Rubel theorem from the 1960s, gives a necessary and sufficient correlation between and , when for each entire function exponential type that vanishes on , there exists an entire function exponential type that vanishes on , with the constraint on the imaginary axis . In subsequent years, this theorem was extended to and , located outside of some pair of angles containing inside. Our version of the Malliavin–Rubel theorem admits the location of and near and on .
ISSN:1066-369X
1934-810X
DOI:10.3103/S1066369X22080072