Constructive Approximation

, Volume 31, Issue 2, pp 259–288 | Cite as

Some Extremal Functions in Fourier Analysis, III

  • Emanuel Carneiro
  • Jeffrey D. Vaaler


We obtain the best approximation in L 1(ℝ), by entire functions of exponential type, for a class of even functions that includes e λ|x|, where λ>0, log |x| and |x| α , where −1<α<1. We also give periodic versions of these results where the approximating functions are trigonometric polynomials of bounded degree.


Approximation Entire functions Exponential type 

Mathematics Subject Classification (2000)

41A30 41A52 42A05 41A05 41A44 42A10 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Texas at AustinAustinUSA

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