Distributions pp 177-220 | Cite as

Fourier Transform

Part of the Cornerstones book series (COR)


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 \(\partial ^\alpha e_\lambda = \lambda ^\alpha e_\lambda\quad (\alpha \in (\mathbf {Z}_{ \ge 0} )^{n}).\)


Fourier Transform Integrable Function Hermite Function Continuous Linear Mapping Linear Partial Differential Operator 
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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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