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1 results

  • 12 - Fourier Series

  • from Part II - Constructive Approximation Theory
  • Abner J. Salgado, University of Tennessee, Knoxville, Steven M. Wise, University of Tennessee, Knoxville
  • Book:
    Classical Numerical Analysis
    Published online:
    29 September 2022
    Print publication:
    20 October 2022, pp 320-344

  • Summary

    This chapter is a close companion to the previous one. Here we study the best least squares approximation to periodic functions via trigonometric polynomials. Many of the ideas and results of the previous chapter are repeated in this scenario. They are then expanded to deal with merely square integrable functions. The Fourier transform of periodic functions, and its inverse, is then introduced and studied. Uniform convergence of trigonometric series, under several different smoothness assumptions is then discussed.Trigonometric approximation in periodic Sobolev spaces is then discussed.