Gap Theorem for Separated Sequences without Pain
Anton Baranov, Yurii Belov, Alexander Ulanovskii
TL;DR
This paper provides a simple proof of the Gap Theorem for separated sequences, utilizing the Beurling--Malliavin formula to clarify the conditions for sequence completeness.
Contribution
It offers a straightforward proof of the Gap Theorem for separated sequences, simplifying previous approaches and applying the Beurling--Malliavin formula.
Findings
Simplified proof of the Gap Theorem
Application of Beurling--Malliavin formula
Enhanced understanding of sequence completeness
Abstract
We give a simple and straightforward proof of the Gap Theorem for separated sequences by A. Poltoratski and M. Mitkovski using the Beurling--Malliavin formula for the radius of completeness.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · advanced mathematical theories · Advanced Harmonic Analysis Research