The Fourier Transform

  • Felipe LinaresEmail author
  • Gustavo PonceEmail author
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 L1(Rn). The case L2(Rn) will be treated in Section 1.2. The space of tempered distributions will be briefly considered in Section 1.3. Finally, in the last two sections we give an introduction to the study of oscillatory integrals in one dimension and some applications.


Fourier Transform Phase Function Initial Value Problem Oscillatory Integral Surjective Isometry 
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Copyright information

© Springer-Verlag New York 2009

Authors and Affiliations

  1. 1.Instituto Nacional deMatemática Pura e Aplicada (IMPA)Rio de Janeiro-RJBrazil
  2. 2.Department MathematicsUniversity of CaliforniaSanta BarbaraUSA

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