Israel Journal of Mathematics

, Volume 114, Issue 1, pp 125–148 | Cite as

Fast decreasing rational functions



Necessary and sufficient conditions are obtained for the existence of sequences of rational functions of the formr n(x) =p n(x)/pn(−x), withp n a polynomial of degreen, that decrease geometrically on (0, 1] in accordance with a specified rate function. The technique of proof involves minimum energy problems for Green potentials in the presence of an external field. Applications are given for the construction of rational approximations of |x| and sgn(x) on [−1, 1] having geometric rates of convergence forx ≠ 0.


Rational Function Maximum Principle Equilibrium Problem Rational Approximation Strict Inequality 
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© Hebrew University 1999

Authors and Affiliations

  1. 1.Department of MathematicsThe Open University of IsraelTel AvivIsrael
  2. 2.Institute for Constructive Mathematics, Department of MathematicsUniversity of South FloridaTampaUSA

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