Constructive Approximation

, Volume 31, Issue 2, pp 259–288

Some Extremal Functions in Fourier Analysis, III

Article

DOI: 10.1007/s00365-009-9050-6

Cite this article as:
Carneiro, E. & Vaaler, J.D. Constr Approx (2010) 31: 259. doi:10.1007/s00365-009-9050-6

Abstract

We obtain the best approximation in L1(ℝ), by entire functions of exponential type, for a class of even functions that includes eλ|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.

Keywords

Approximation Entire functions Exponential type 

Mathematics Subject Classification (2000)

41A30 41A52 42A05 41A05 41A44 42A10 

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Texas at AustinAustinUSA

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