Fourier sums in weighted spaces of functions. A survey

• G. Mastroianni ^[1] ; M. G. Russo ^[1]
  1. [1] Università della Basilicata

     Università della Basilicata

     Potenza, Italia

     
• Localización: Jaen journal on approximation, ISSN 1889-3066, ISSN-e 1989-7251, Vol. 1, Nº. 2, 2009, págs. 257-291
• Idioma: inglés
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• Resumen

  • This survey is devoted to the study of the behaviour of the Fourier sums in weighted spaces of functions. The cases of functions supported on bounded or unbounded intervals of the real line are investigated. In particular the proof of the Riesz theorem is extended to the case of Fourier sums in systems of suitable orthonormal polynomials.