Israel Journal of Mathematics

, Volume 153, Issue 1, pp 193–219 | Cite as

Jackson and Bernstein theorems for the weight exp(−|x|) on ℝ

  • D. S. Lubinsky


In 1978, Freud, Giroux and Rahman established a weightedL 1 Jackson theorem for the weight exp(−|x|) on the real line, using methods that work only inL 1. This weight is somewhat exceptional, for it sits on the boundary between weights like exp(-|x|α), α≥1, where weighted polynomials are dense, and the case α<1, where weighted polynomials are not dense. We obtain the firstL p Jackson theorem for exp(−|x|), valid in allL p , 0<p≤∞, as well as for higher order moduli of continuity. We also establish a converse Bernstein type theorem, characterizing rates of approximation in terms of smoothness of the approximated function.


Orthogonal Polynomial Polynomial Approximation Exponential Weight Constructive Approximation BERNSTEIN Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Hebrew University 2006

Authors and Affiliations

  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

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