Bounded Power Series on the Real Line

• DOI: 10.48550/arxiv.2312.09267
• Publication Date: 2023-01-01
• Authors: Davide Sclosa
• Keywords: Real line; Line (geometry)

We investigate power series that converge to a bounded function on the real line. First, we establish relations between coefficients of and boundedness resulting function; in particular, show can be prevented by certain Tur\'an inequalities and, case coefficients, sign patterns. Second, set naturally supports three topologies these are inequivalent incomplete. In each case, determine topological completion. Third, study algebra series, revealing key role backward shift operator.