• Corpus ID: 118898111

$(s,p)$-Valent Functions

@article{Friedland2015spValentF,
  title={\$(s,p)\$-Valent Functions},
  author={Omer Friedland and Yosef Yomdin},
  journal={arXiv: Classical Analysis and ODEs},
  year={2015}
}
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… 
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For an analytic function $f(z)=\sum_{k=0}^\infty a_kz^k$ on a neighbourhood of a closed disc $D\subset {\bf C}$, we give assumptions, in terms of the Taylor coefficients $a_k$ of $f$, under which the
NORMING SETS AND RELATED REMEZ-TYPE INEQUALITIES
The classical Remez inequality [‘Sur une propriété des polynomes de Tchebycheff’, Comm. Inst. Sci. Kharkov13 (1936), 9–95] bounds the maximum of the absolute value of a real polynomial $P$ of degree

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