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 \(\partial ^\alpha e_\lambda = \lambda ^\alpha e_\lambda\quad (\alpha \in (\mathbf {Z}_{ \ge 0} )^{n}).\)
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Duistermaat, J.J., Kolk, J.A.C. (2010). Fourier Transform. In: Distributions. Cornerstones. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4675-2_14
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DOI: https://doi.org/10.1007/978-0-8176-4675-2_14
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