Littlewood-type Problems on Subarcs of the Unit Circle

@inproceedings{Borwein1997LittlewoodtypePO,
  title={Littlewood-type Problems on Subarcs of the Unit Circle},
  author={Peter Borwein and Tam{\'a}s Erd{\'e}lyi},
  year={1997}
}
The results of this paper show that many types of polynomials cannot be small on subarcs of the unit circle in the complex plane. A typical result of the paper is the following. Let Fn denote the set of polynomials of degree at most n with coefficients from {−1, 0, 1}. There are absolute constants c1 > 0, c2 > 0, and c3 > 0 such that exp (−c1/a) ≤ inf 06=p∈Fn ‖p‖L1(A) , inf 06=p∈Fn ‖p‖A ≤ exp (−c2/a) for every subarc A of the unit circle ∂D := {z ∈ C : |z| = 1} with length 0 < a < c3. The lower… CONTINUE READING
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