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 pn(z) = zn+...+an, is true that the length of the lemniscate |pn(z)| = 1 is maximal if pn(z) = zn-1? Let -1 \leq x1 < ... < xn \leq 1 and denote the fundamental polynomial of Langrange interpolation by lk(x): lk(xk) = 1, lk(xj) = 0 for 1 \leq j \leq n, j\neq k. Is it true that there exists a point system {xj(n)} such that for every x0, limsupn ––> oosumj = 1nlj(n)(x0) = oo but for every continous function f there is a Y0 such that sumj = 1nf(xj(n))lj(n)(y0) ––> f(y0) 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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