Products of Polynomials in Uniform Norms

  title={Products of Polynomials in Uniform Norms},
  author={Igor E. Pritsker},
We study inequalities connecting a product of uniform norms of polynomials with the norm of their product This subject includes the well known Gel fond Mahler inequalities for the unit disk and Kneser inequality for the segment Using tools of complex analysis and potential theory we prove a sharp inequality for norms of products of algebraic polynomials over an arbitrary compact set of positive logarithmic capacity in the complex plane The above classical results are contained in our theorem as… CONTINUE READING