A Characterization of One-component Inner Functions
| Autor: | Atte Reijonen, Artur Nicolau |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Mathematics - Complex Variables General Mathematics Blaschke product 010102 general mathematics Singular measure Function (mathematics) Characterization (mathematics) 01 natural sciences Null set Set (abstract data type) symbols.namesake Mathematics - Classical Analysis and ODEs Component (UML) symbols Classical Analysis and ODEs (math.CA) FOS: Mathematics 0101 mathematics Complex Variables (math.CV) 30J05 30J10 30J15 Mathematics |
| DOI: | 10.48550/arxiv.2001.05188 |
| Popis: | We present a characterization of one-component inner functions in terms of the location of their zeros and their associated singular measure. As consequence we answer several questions posed by J. Cima and R. Mortini. In particular we prove that for any inner function $\Theta$ whose singular set has measure zero, one can find a Blaschke product $B$ such that $\Theta B$ is one-component. We also obtain a characterization of one-component singular inner functions which is used to produce examples of discrete and continuous one-component singular inner functions. Comment: 10 pages, 3 figures |
| Databáze: | OpenAIRE |
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