Introduction to Harmonic Analysis

  • Elena Prestini
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


“The eighteenth century stands out in mathematical history as an era of great genius. Through the work of anastonishing array of masters the science was extended and broadened by the opening of many new fields. Technical skill attained to extraordinary high levels and new ideas were crowded one upon the other” (Langer [1947]). The subject of trigonometric series received much attention: it was stated that they could represent “any” function, and formulas were found, but agreement among the masters of the time was not there. It must be said that the issues were far from simple. The tricky one of computations dealing with infinitely many terms, around which much of calculus revolves, was not being properly investigated and clearly regulated. The notion of the sum of infinitely many terms was imprecise; as if no different from the finite case, it was a common practice to rearrange terms infinitely many times as well as to integrate and differentiate term by term infinitely many times.


Harmonic Analysis Fourier Series Heat Diffusion Trigonometric Series Rectangular Pulse 
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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Elena Prestini
    • 1
  1. 1.Department of MathematicsUniversity of Rome “Tor Vergata”RomeItaly

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