Kaplan classes of a certain family of functions | Zendy

Szymon Ignaciuk | Zendy; Maciej Parol | Zendy

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Kaplan classes of a certain family of functions

Author(s) -

Szymon Ignaciuk,

Maciej Parol

Publication year - 2020

Publication title -

annales universitatis mariae curie-sklodowska sectio a – mathematica

Language(s) - English

Resource type - Journals

eISSN - 2083-7402

pISSN - 0365-1029

DOI - 10.17951/a.2020.74.2.31-40

Subject(s) - monotonic function , characterization (materials science) , sequence (biology) , mathematics , power (physics) , class (philosophy) , combinatorics , pure mathematics , discrete mathematics , function (biology) , physics , mathematical analysis , computer science , chemistry , quantum mechanics , biochemistry , artificial intelligence , optics , evolutionary biology , biology

We give the complete characterization of members of Kaplan classes of products of power functions with all zeros symmetrically distributed in \(\mathbb{T} := \{z \in\mathbb{C} : |z| = 1\}\) and weakly monotonic sequence of powers. In this way we extend Sheil-Small’s theorem. We apply the obtained result to study univalence of antiderivative of these products of power functions.

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