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Distributions pp 177-220 | Cite as

Fourier Transform

  • J. J. Duistermaat
  • J. A. C. Kolk
Chapter
Part of the Cornerstones book series (COR)

Abstract

Let \(\lambda \in \mathbf {C}^{n}.\) The function \(e_\lambda :x \mapsto e^{\left\langle {x,\lambda } \right\rangle } = e^{x1\lambda 1 + \cdots + x_n \lambda _n }\) in \({C}^\infty (\rm \mathbf {R}^n )\) has the remarkable property that \(\partial ^\alpha e_\lambda = \lambda ^\alpha e_\lambda\quad (\alpha \in (\mathbf {Z}_{ \ge 0} )^{n}).\)

Keywords

Fourier Transform Integrable Function Hermite Function Continuous Linear Mapping Linear Partial Differential Operator 
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 Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Mathematical InstituteUtrecht UniversityUtrechtThe Netherlands

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