Set of uniqueness for Cantorvals
Szymon Glab, Jacek Marchwicki
TL;DR
This paper investigates the set of uniqueness in Cantorvals, showing that the Guthrie-Nymann Cantorval has a comeager set of uniqueness, while many other Cantorvals have meager sets of uniqueness.
Contribution
It establishes the contrasting properties of the set of uniqueness across different Cantorvals, highlighting the special case of the Guthrie-Nymann Cantorval.
Findings
Guthrie-Nymann Cantorval has a comeager set of uniqueness.
Many other Cantorvals have a meager set of uniqueness.
The set of uniqueness varies significantly among different Cantorvals.
Abstract
The main result is that the celebrated Guthrie-Nymann's Cantorval has comeager set of uniqueness. On the other hand many other Cantorvals have meager set of uniqueness.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Functional Equations Stability Results · Meromorphic and Entire Functions