Harmonic Analysis in Euclidean Space

  • Jayakumar Ramanathan
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


The ideas that led to the representation of periodic functions as trigonometric series will be applied to functions defined on Rn. As before, we will attempt to expand functions in terms of characters parameterized, however, by Rn instead of Z. As a consequence, series expansions will be replaced by integral expansions, and the theory of inversion will have a different flavor than in the previous case. However, the underlying themes in this chapter will be the same as those of chapter 2: convolution and approximation, Plancherel’s theorem, Bochner’s theorem etc.


Fourier Transform EUCLIDEAN Space Harmonic Analysis Integrable Function Triangle Inequality 
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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Jayakumar Ramanathan
    • 1
  1. 1.Department of MathematicsEastern Michigan UniversityYpsilantiUSA

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