科研之友
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摘要
A few years ago, the second named author was asked if he knew the largest open simply connected region G(n) superset of [-1, 1] containing no zero of any polynomial p of degree n is an element of N such that 0 < m <= vertical bar p(x)vertical bar <= M for all x is an element of [-1, 1]. This question is answered in Theorem 3. This required us to first consider a related problem for polynomials on the unit circle, whose solution is given in Theorem 1. The paper contains several other results which are all sharp.
- 出版日期2014
