The Fourier Transform

  • Felipe LinaresEmail author
  • Gustavo Ponce
Part of the Universitext book series (UTX)


In this chapter, we shall study some basic properties of the Fourier transform. Section 1.1 is concerned with its definition and properties in \(L^1(\mathbb{R}^n)\). The case \(L^2(\mathbb{R}^n)\;\) is considered in Section 1.2. The space of tempered distributions is briefly considered in Section 1.3. Finally, Sections 1.4 and 1.5 give an introduction to the study of oscillatory integrals in one dimension and some applications, respectively.

Copyright information

© Springer-Verlag New York 2015

Authors and Affiliations

  1. 1.Instituto Nacional de Matemática Pura e Aplicada (IMPA)Rio de JaneiroBrazil
  2. 2.Dept. MathematicsUniversity of California, Santa Barbara College of Letters & ScienceSanta BarbaraUSA

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