$(s,p)$-Valent Functions
| Autor: | Friedland, Omer, Yomdin, Yosef |
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| Rok vydání: | 2015 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We introduce the notion of $(\mathcal F,p)$-valent functions. We concentrate in our investigation on the case, where $\mathcal F$ is the class of polynomials of degree at most $s$. These functions, which we call $(s,p)$-valent functions, provide a natural generalization of $p$-valent functions (see~\cite{Ha}). We provide a rather accurate characterizing of $(s,p)$-valent functions in terms of their Taylor coefficients, through "Taylor domination", and through linear non-stationary recurrences with uniformly bounded coefficients. We prove a "distortion theorem" for such functions, comparing them with polynomials sharing their zeroes, and obtain an essentially sharp Remez-type inequality in the spirit of~\cite{Y3} for complex polynomials of one variable. Finally, based on these results, we present a Remez-type inequality for $(s,p)$-valent functions. Comment: arXiv admin note: text overlap with arXiv:1102.2580 |
| Databáze: | arXiv |
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