Loomis Type Theorem for Bounded Sequences
Year: 2026
Type: article
Abstract: This paper extends Loomis’s classical spectral criterion for almost periodic functions to bounded sequences in discrete settings. We first establish a discrete Kadets-type theorem for bounded sequences by regarding almost periodic functions as continuous with respect to the Bohr metric. We then introduce three spectra for bounded sequences via the Carleman transform and prove their equivalence. Using the Beurling–Gelfand theorem, we derive a discrete Loomis-type theorem, providing a spectral criterion for almost periodicity of bounded sequences. Our results extend the continuous theory to the discrete case and offer new tools for analyzing almost periodicity in sequence spaces.
Source: Axioms
Authors: Yuan-Yuan Chen, Wei-Gang Jian, Hai-Ping Zhong
Institution: Yuzhang Normal University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
OpenAlex ID: W7161553543
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