• Corpus ID: 233296391

# Note on Spectral Factorization Results of Krein and Levin

@inproceedings{Lawton2021NoteOS,
title={Note on Spectral Factorization Results of Krein and Levin},
author={Wayne M. Lawton},
year={2021}
}
Bohr proved that a uniformly almost periodic function f has a bounded spectrum if and only if it extends to an entire function F of exponential type τ(F ) < ∞. If f ≥ 0 then a result of Krein implies that f admits a factorization f = |s|2 where s extends to an entire function S of exponential type τ(S) = τ(F )/2 having no zeros in the open upper half plane. The spectral factor s is unique up to a multiplicative factor having modulus 1. Krein and Levin constructed f such that s is not uniformly…

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