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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 494.30002

**Autor: ** Erdös, Paul

**Title: ** Problems and results on polynomials and interpolation. (In English)

**Source: ** Aspects of contemporary complex analysis, Proc. instr. Conf., Durham/Engl. 1979, 383-391 (1980).

**Review: ** [For the entire collection see Zbl 483.00007.]

In this paper many problems and results on polynomials and interpolation are descibed and a survey of the last development of this subject is given. To give an example we present two of these problems: Let p_{n}(z) = z^{n}+...+a_{n}, is true that the length of the lemniscate |p_{n}(z)| = 1 is maximal if p_{n}(z) = z^{n}-1? Let -1 \leq x_{1} < ... < x_{n} \leq 1 and denote the fundamental polynomial of Langrange interpolation by l_{k}(x): l_{k}(x_{k}) = 1, l_{k}(x_{j}) = 0 for 1 \leq j \leq n, j\neq k. Is it true that there exists a point system **{**x_{j}^{(n)}**}** such that for every x_{0}, **limsup**_{n ––> oo}**sum**_{j = 1}^{n}l_{j}^{(n)}(x_{0}) = oo but for every continous function f there is a Y_{0} such that **sum**_{j = 1}^{n}f(x_{j}^{(n)})l_{j}^{(n)}(y_{0}) ––> f(y_{0}) for n ––> oo?

**Reviewer: ** M.Menke

**Classif.: ** * 30-02 Research monographs (functions of one complex variable)

30C10 Polynomials (one complex variable)

30E05 Moment problems, etc.

00A07 Problem books

**Keywords: ** problems and results on polynomials and interpolation

**Citations: ** Zbl.483.00007

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