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The Fourier Transform

  • Felipe Linares
  • Gustavo Ponce
Chapter
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.

Keywords

Fourier Transform Phase Function Initial Value Problem Oscillatory Integral Surjective Isometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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