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Asymptotics of Fourier Transforms

  • Alexander I. SaichevEmail author
  • Wojbor Woyczynski
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

In Chapter 3 we demonstrated that the Fourier transform \( \tilde{f}(\omega ) \) of a smooth function f(t) rapidly decays to zero as ω →∞. However, smoothness is rare in natural phenomena and one often encounters processes that are either discontinuous or violate the smoothness assumption in other ways. Such phenomena include, for example, shock fronts generated by large amplitude acoustic waves, ocean waves, or desert dunes with their characteristic sharp crests.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Mathematical DepartmentState University of Nizhny NovgorodNizhny NovgorodRussia
  2. 2.Math, Applied Math, & Stat, Yost 229Case Western Reserve UniversityClevelandUSA

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